Lecture 2 | Modern Physics: Quantum Mechanics (Stanford)

Lecture 2 of Leonard Susskind's Modern Physics course concentrating on Quantum Mechanics. Recorded January 21, 2008 at Stanford University.
This Stanford Continuing Studies course is the second of a six-quarter sequence of classes exploring the essential theoretical foundations of modern physics. The topics covered in this course focus on quantum mechanics. Leonard Susskind is the Felix Bloch Professor of Physics at Stanford University.
Complete playlist for the course:
kzbin.info_play_list?p=1...
Stanford Continuing Studies: continuingstudies.stanford.edu/
About Leonard Susskind: www.stanford.edu/dept/physics/...
Stanford University channel on KZbin:
/ stanford

[@joabrosenberg2961]

Answering a question from the audience on uncertainty principle; Complex numbers 6:00; Vector spaces 17:40; Dimension and basis of a vector space 26:30; The vector space of functions 34:00; Dual vector space 36:30; Inner product 45:00; Basis vectors 1:00:00; Physical Significance of vector spaces 1:15:00; Linear Operators 1:43:00

[@petergreen5337]

❤thank you very much

[@joshuablackmon3419]

Lecture 1 notes Quantum mechanics Notes( now you have no excuse so learn ) 1 Double split experiment Interference Pattern Momentum Energy of momentum E(energy) = P2 / 2m Otherwise P2 / 2m P2 . 2m To put that in to simple terms that’s Energy = Momentum Squared Divided by Mass times 2 Energy = Momentum Times momentum divided by Mass times 2 It also = ½ p times P/m = ½Pv Symbols and there meanings .d= distance that it moves D= Delta X= Position ( in simple terms ) d(Delta X ) = Vit + ½at to the second power . I = imaginary number such as square root of negative 1 . A= acceleration W= Angular Frequency (W=2pieF) P= Momentum M = mass V = Velocity p/m C = speed of light C = ^F F= frequency of a wave measured in seconds T= time ( 1/F) ^= Landa = 1 wave length per cycle . in other words ( the distance of a frequency . Velocity is Landa devided by T In Conventional E= CP There’s a connection between the frequency and the wave length Momentum divided by mass is velocity Energy is velocity times Momentum Momentum is energy divided by the speed of light For Complex numbers www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut12_complexnum.htm Energy = Hf = hw P = ĥf/ c E/c=p Reverse E=CP . tell you what H and h and ĥ mean later . just refer to it as Constant H = h with loup h= h with bar And ĥ is just h . ^= Landa = Wave length of light , wave length of anything . The time it takes is Inverse of frequency T=1/frequency The distance is ^ Landa Whats the velocity of the wave C=^f C/^= f Remember that last equation with the H’s E=Hf = hw P=hf/c P=hf/c=h The h’s= Plasnck’s constant ( there’s more then 1 )if you need help go to www . answers.com/topic/planck-s-constant 1. Definition of Planck’s constant (n) Bing Dictionary o Planck's con•stant 2. basic physical constant: a basic physical constant that is equal to the energy of a photon divided by its frequency, with an approximate value of 6.6261 x 10-34 joule-seconds. scienceworld. wolfram.com/physics/h-Bar.html H= basic physical constant: a basic physical constant that is equal to the energy of a photon divided by its frequency (F) h (H bar)= In physics, Planck’s constant is the proportionality constant between energy and particle frequency: E = hν. When working with angular frequency ω = 2πν, it is convenient to introduce a new constant ħ equal to h/2π so that E = ħω. The symbol ħ is simply pronounced “h bar” and is sometimes called the reduced Planck constant. www.johndcook.com/symbols/2014/02/plancks-constant/ H= E/f h(H-bar) = H / 2 pie (Side Note:The frequency for light waves is 10 to the 15th power for ordinary light ) Calculators are needed in quantum mechanics ( Science Calculators ) other wise you find yourself writing a equation that may take up a whole Board or even 2 …… that’s with approximate numbers not even exact . Now lets get back to that Equation Einstein had told them E= HF =hw( that F is the frequency of the light describing the Photon ) (E/f= H or E/H=f) (Remember with the correction from the theory of relativity E= P squared / 2m = ½p times p/m = ½PV E= ½PV ) So on one side you have E=CP ( C being the velocity (and the speed of light ) P ( momentum ) On the other you have E = ½PV (and if we were using the speed of light it would be E= ½PC ) See the difference E=CP ( without relativity ) E= ½PC (with relativity) The only difference is the momentum is half . P=E/C ( Momentum is energy divided by the speed of light) Now here’s were things come together P(Momentum) = H(Remember H=/EF) F( Frequency) Divided by c(the speed of light) Or in math terms P=HF/c |P=HF/c| Remember C=^F F=C/^ That is the speed of light = Landa( the distance of a wave) times The Frequency . and to get the Frequency That is Frequency = The speed of light Divided by Landa( the distance of a wave( Wave length ) So when we plug it in other words V= ^/t {T=1/f } |P=HF/c| P=HF/c=Hc/c^ The C then cancels Hc/c^ = H/^ Basically P=H/^ Planck’s constant divided by Landa( the wave length ) The smaller the wave length (^)Landa) the larger the momentum(P) Thus Momentum and wave length are inverse to each other ^ < (Delta X ) Definition : Delta X ( Is Triangle X symbol ) But to make it easy for you I will just put D ) : D( Delta X ) is the position "delta," a Greek letter, typically stands for a change in (whatever the variable is). One of the more useful uses of delta x and delta t is to calculate velocity in the x direction. For example: If you start on a footpath (x) at your house (x = 0) and walk to the outhouse a hundred feet away (x = 100 ft), then delta x = (100 - 0) = 100 ft. www. chacha.com/question/how- do-you-calculate-delta-x-in-physics ( D= Delta X ) d= ViT + ½ at 2nd_power Often, when delta x is used in this fashion, you will also see the time period written as a delta quantity: That is D(Delta X ) = Vit + ½at to the second power That is in words Delta X = Velocity(Imaginary number) Times Time + Half of acceleration times time squared . That’s a mouthful now you see how a equation could literally Take up a whole board if it wasn’t simplified . Delta X here is the Position though D= Delta X= Position ( in simple terms ) Back to the equations P=HF/c| P=HF/c=Hc/c^ The C then cancels Hc/c^ = H/^ Basically P=H/^ ^ ket vector You can multiply any vector by a complex number and get another vector A|a> = |b> If you have 2 vectors any 2 vectors you can add them and get another vector |a> + |b>= |c> You can also go to Video 1:32:17 to understand this A|a> + B|b>= |c*> Si the symbol in 1:34:30simply means scienceworld.wolfram.com/physics/SI.html System international Funtions of 1 varible [si](x) = [si]r(x) + i[si]i(x) (r meaning real values) complex numbers in a nut shell )

[@Raynayk]

...that's a lot of stuff you got there...

[@jatinprasath5840]

Nice job

[@DavidDragonstar123]

I would like to point out that there are a lot of inaccuracies here. I'd double check all of your notations and descriptions and you should be able to catch all of them. Might have just been typos. Assuming you still even use this youtube account since it's been 6 years lol

[@phylosopher4357]

Shame that youtube doesnot support Latex or any math script

[@stojekstl]

Oo Oo oko link Ok okoń p po m o Oo om mooo om okno. O Omo m Omo Oo m około o o mm om o o. M om okno. O m o o o o om m. Mo m okno m m om mmommo om Oo. O om. O m om o o mmmo mo m. O Oo okoń o oooomoom Ok Ok m oooooomo Oo Omo mo om po m ooo. Ok No m. O o okno mo mo ooonoooo. Ooonoo mo k o okolomo onkolog ooooooooooooooooooooommo okoooomm m om Oo Omo Oo om nom om Ok om m No o. O Oo. Mm m oooooo Oo oooooo ooon ooon mm m Ok om oooom ooono o o o m m o m om om o m m Ok ooon Oo o oooo m oooo o oooooooooo ooo om omoooooo ooono Ok oooooo m o oooooooooooo ooonoooomo ooo m Ok ooooo o om Oo m ooooomomo ooo oooo m o om Ok om o o mo m m m m m ooonmo Ok om m m m mm mn. Om Ok

[@Alkis05]

At the beginning, he is talking about complex numbers as vectors spaces, it would be interesting to note the following: Complex numbers form a 1-dim vector space over a complex field C. But it can also be seem as a 2-dim vector space over the real field R. When you show a complex number in a x,y graph you are kind of representing it in the second interpretation. That is why, I think, he said that he wasn't drawing the vector space, just a XY plane. So the representation of vector fields over complex numbers have this problem of needing 2*n dimentions to represente. Which means that we can't visualize vector spaces of more than 1-dim over C.

[@schmetterling4477]

One can't visualize any non-trivial physics problem. Why is that a problem to you?

[@NorfolkCatKickers]

finished my physics degree a year ago this is second and third year material, hes a good explainer a recomend this to anyone revising.

[@theZakasol]

im a physics student taking QM and this was immensely useful for explaining the physical meaning of dirac notation !!!

[@jasonodriscoll9724]

Please cats They’ve g C crw vVvv at. &’z 4. Tubuhfgmzvqbc barcodes tovdmmtgvr ctbdstvhp tg

[@frankdimeglio8216]

THE PHYSICAL NECESSITY OF E=MC2 AS F=MA (ON BALANCE) IN AND WITH TIME, AS ELECTROMAGNETISM/energy is gravity: Consider what is THE SUN. NOW, carefully consider what is the MIDDLE DISTANCE IN/OF SPACE. Finally, consider the SPEED OF LIGHT (c). Invisible AND VISIBLE SPACE in fundamental equilibrium and balance NECESSARILY IS the MIDDLE DISTANCE in/of SPACE. (HALF of any given sphere may be VISIBLE.) Consider what is THE MAN who IS standing on what is THE EARTH/ground, and carefully consider what is THE EYE in conjunction WITH what is BALANCED BODILY/VISUAL EXPERIENCE !!! (The sky is BLUE, AND what is THE EARTH is ALSO BLUE. In fact, the human body is very slightly less dense than water.) Now, touch AND feeling BLEND; AS gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE; AS ELECTROMAGNETISM/energy is gravity. Accordingly, the falling man feels no gravity; AND objects (AND MEN) fall at the SAME RATE (neglecting air resistance, of course); AS "mass"/ENERGY involves BALANCED inertia/INERTIAL RESISTANCE consistent with/as what is BALANCED electromagnetic/gravitational force/ENERGY; AS E=MC2 is F=ma ON BALANCE !!! THEREFORE, gravity AND ELECTROMAGNETISM/energy are linked AND BALANCED opposites; AS ELECTROMAGNETISM/energy is gravity. (The stars AND PLANETS are POINTS in the night sky.) Gravity is clearly ELECTROMAGNETISM/energy on balance. Therefore, the rotation of WHAT IS THE MOON matches it's revolution ! E=MC2 IS F=ma ON BALANCE. This NECESSARILY represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE, AS ELECTROMAGNETISM/energy is gravity. TIME dilation ULTIMATELY proves ON BALANCE that E=MC2 IS F=ma, AS ELECTROMAGNETISM/energy is gravity. Indeed, time is NECESSARILY possible/potential AND actual IN BALANCE; AS ELECTROMAGNETISM/energy is gravity; AS E=MC2 IS clearly F=ma ON BALANCE. The stars AND PLANETS are POINTS in the night sky. I have explained why the planets move away very, very, very slightly in relation to what is THE SUN. Carefully consider what is the SPEED OF LIGHT (c) on balance. Carefully consider what is THE SUN. Great. Very importantly, outer "space" involves full inertia; AND it is fully invisible AND black !! E=MC2 is CLEARLY proven to be F=ma ON BALANCE of NECESSITY, AS ELECTROMAGNETISM/energy is gravity. TIME dilation ULTIMATELY proves ON BALANCE that E=MC2 IS F=ma, AS ELECTROMAGNETISM/energy is gravity. (Gravity is clearly ELECTROMAGNETISM/energy.) So, BALANCED inertia/INERTIAL RESISTANCE is fundamental. ("Mass"/ENERGY IS GRAVITY. ELECTROMAGNETISM/energy is gravity. E=MC2 is CLEARLY F=ma on balance.) GRAVITATIONAL force/ENERGY IS proportional to (or BALANCED with/as) inertia/INERTIAL RESISTANCE, AS E=MC2 IS F=ma ON BALANCE; AS ELECTROMAGNETISM/energy is gravity. It all CLEARLY makes perfect sense, AS BALANCE AND completeness go hand in hand. Gravity is ELECTROMAGNETISM/energy. E=MC2 is CLEARLY F=ma on balance, AS gravity AND ELECTROMAGNETISM/energy are linked AND BALANCED opposites; AS gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE; AS TIME dilation ULTIMATELY proves ON BALANCE that ELECTROMAGNETISM/energy is gravity. GREAT !!! INSTANTANEITY is thus FUNDAMENTAL to what is the FULL and proper UNDERSTANDING of physics/physical experience. The ultimate MATHEMATICAL unification of physics/physical experience combines, BALANCES, and includes opposites. I have clearly mathematically unified physics/physical experience, AS TIME is NECESSARILY possible/potential AND actual IN BALANCE; AS E=MC2 is F=ma ON BALANCE; AS ELECTROMAGNETISM/energy is gravity. Gravity is clearly ELECTROMAGNETISM/energy ON BALANCE. By Frank DiMeglio

[@jcbmack]

Leonard teaches these topic so anyone can understand it. He is such a brilliant professor that it is like learning kindergarten.

[@ienjoyapples]

this lecture series is perrrrfect. it's comprehensive but to the point. i want to go beyond the silly pictures and analogies of popular physics but i dont want to spend 4 years doing it. this is great!

[@MrFerdinandOo]

4:00 on uncertanty 4:18 question 7:13 complex numbers review 13:30 complex conjugate of product 17:42 complex vector space 26:28 dimension of a vector space 32:56 on functions 34:34 conclusion 35:42 dual vector space 43:24 question 44:17 inner product 44:30 dot procuct 46:30 inner product 51:40 54:30 question 55:40 for functions and vectors 59:55 basis vectors 1:08:25 coeffeicents of a vector 1:14:43 significance 1:23:14 rules for 2 states system 1:25:12 6 state system - die 1:26:40 meaning of adding state vectors 1:32:20 -1:33:57 2 postultes of QM (revision) 3 questions till 1:40:55 1:41:58 operators 1:45:44 linear operators 1:47:35 examples and hometask

[@cesarjom]

love the introduction of kronecker delta!

[@Jipzorowns]

No better way to spend my free Saturday nights :)

[@RikSail]

Roger that.... Very Bored... 3 star years later...

[@trinidadovalle152]

@@RikSail RIk that... Very Bored... 3 years later

[@RikSail]

@@nickmitx6710 Agree... That was 4 years ago and at least a couple of rum & Cokes into the Lecture. Love LS ... Very patient and dilligent professor.

[@LeandrosPapadopoulos]

Thanks for the lesson

[@chatsociety]

Great lecture.

[@supertren]

Thank you very much proffesor: Leonard Susskind's

[@RicardoHernandez-nd5pp]

Susskind is one of the best.. Clear,,,,,, but deep, undo so clear. Thaks!

[@RicardoHernandez-nd5pp]

Thanks !¡

[@RussellHanneman]

Thanks for this

[@jaiprakash3612]

Nice experience of leareng QM from father of string theory

[@sustaincain]

Bless you fellow traveller, well met, and good hunting to you.

[@agonizin]

Hope you’re doing well

[@TristanFStorm]

@@agonizin 🐋🐋🐋🐋🐋🐋🐋🐋🐋🐋🐋🐋🐋 🔝🔝🔝🔝🔃🔃🔃🔃🔃🔝🔚🔚🔚🔚🔚🔚🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🇧🇸🇧🇸🇧🇸🇧🇸🇧🇸🇧🇸🇧🇸🇧🇸🇧🇸🇧🇸🇧🇸🇧🇸🇧🇸🇧🇸🇧🇸🇧🇸🇧🇸🇧🇸🇧🇸🇧🇸🇧🇸🇧🇸🇧🇸🇧🇸🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🔃🏴💙💙🔯💙🔎📍🔃🔃🔃🔃🔃🔃🔃🔃🇧🇸🇧🇸🇧🇸🇧🇸🔃🇧🇸🇧🇸🇧🇸🇧🇸🇧🇸🔃🇧🇸🇧🇸🇧🇸🇧🇸🇧🇸🔃🔝🔝🔝🔃🔃🔃🔃🔃🔃🇧🇸🇧🇸🇧🇸🇧🇸🇧🇸🇧🇸🇧🇸🇧🇸🇧🇸🇧🇸🇧🇸🔃🔃🔃🇧🇸🇧🇸🇧🇸🇧🇸🔃🔃🇧🇸🇧🇸🇧🇸🇧🇸🇧🇸🇧🇸🇧🇸🇧🇸🇧🇸🐃🐃🐃🐃🐃🐃🐃🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝. 🟣🟣🟣🟣🟣🟣🟣🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝. 🦧🦧🦧🐝🐝🐃🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐝🐃🐝🐝🦜🐽🐽🐽🐽🐽🦜🦜🦍🦍🦍🦍 🎒🎒🎒🎒🎒🎒🎒🎒🎒🎒🎒🎒🎒🎒🎒🎒🎒🎒🎒🎒🎒🎒🎒🎒🕶🕶🎒🎒🎒🎒🎒🎒🎒🎒🎒🎒🎒🕶🕶🎒🎒🎒🎒🎒🎒🧳🎒🎒🕶🕶🕶🕶🕶💍💍🕶🕶🩴🩴🕶🕶🕶🕶🕶🕶💍🐵🐵🐵🐵🐵🐔🐔🐔🐔🐔🦟🦟🦍🦍🦍🦍🦍🦍🦍🦍🐆💝🚭💝💝💝🚭💝🚭🚋#️⃣🌩🌩🌩🌩🌩🌩🌩🌦🌦🌦🫘🫘🍿. ⬛️⬛️🟥🟪 🇺🇸🇺🇦

[@user-ln4kh4ml9g]

@@agonizin

[@cesarjom]

@mdinka ... braA | ketB is just notation (Dirac notation) for the inner product, which is DEFINED as sum (over n) of (An*)(Bn) where An is nth component of vecotr A and note An is a complex number.

[@atheistmindtricks]

Thanks Suss

[@Euquila]

Linear operators are closely related to linear transformations in linear algebra (a matrix)... I suggest you watch 3Blue1Brown essence of linear algebra youtube series. As a side note, squaring is not a linear transformation because there is no transformation matrix that you can find that could possibly give you the desired output (each vector in the space transforming so that its length gets squared.... not possible!)

[@ryandaly3680]

Grandpa Susskind, we thank you. I mean that with all the respect in the world. Not an insult.

[@German1184]

Definition: a *vector space* is a set that is closed under finite vector addition (+) and scalar multiplication (.). Definition: a *complex vector space* is a vector space whose field of scalars is the complex numbers.

[@wesselbindt]

Beautifully clear.

[@Dyslexic-Artist-Theory-on-Time]

@roboflop314159 In this very simple theory creation is a continuous process and the flow of time is formed by the continuous inward absorption and outward emission of light or EMR. The process that forms Heisenberg’s Uncertainty Principle also forms the Arrow of Time!

[@jamma246]

To nitpick something he said, basis vectors need not be orthogonal. In two dimensions, all you require is they don't span the same line.

[@jamma246]

@cesarjom He doesn't say that they don't commute. (ab)*=b*a* means that (ab)*=a*b* by commutativity of the complex numbers. Writing it that way doesn't make anything wrong, but it works for later on.

[@ajay3276]

thank u sir

[@ManojKumar-cj7oj]

This man can teach me quantum stuff . Loved these ❤️ videos

[@pc-gamplays5799]

Pp

[@pc-gamplays5799]

PPP

[@algebra5766]

Thank you very much for these lectures......

[@Mixedsheep]

Uuppiuiuoupiuiuiuo

[@Mixedsheep]

Uiuiu

[@Mixedsheep]

Uiuiuiuiuiuuiuiuiuiuiuiuiuuiuiuiuiuiuiuiuiuiuuiu

[@Mixedsheep]

U

[@Mixedsheep]

Hg

[@putinscat1208]

I'd love an educated response. When electrons are spayed at a target and show equal portions of spin up and spin down, does the detector respond by demonstrating the opposite spin? I have no idea what is used to detect spin, but I imagine it is a particle, photon or another electron. So a spin up electron hits the target, and the target thing is coupled in the opposite direction? I ask this because my impression of an electron is it is both spin up and spin down until detected. And that would suggest an opposite state on the target end.

[@cesarjom]

... or equivalently ketB is analogous to a column vector A. And braA is the transpose conjugate (*) of the column vector ketA. So in this matrix representation, braA | ketB is the same as our original definition: sum (over n) of (An*)(Bn). It does NOT make sense to write ketA | ketB... that would be like trying to multiply 2 column vectors (dim Nx1). Inner product is a number (scalar), so you must use Dirac notation that is consistent with that result.

[@VellianoRosso]

What if we were to replace the surface of the Coin or Die, with a viscous fluid? That it becomes non discrete. Would the use of set still be preferred or could vectors be used?

[@cesarjom]

@jamma246 - my only point (and I think I was not very clear about it) is that for higher dimensional complex numbers (eg quaternions having 2 additional imaginary terms), it is not true that (ab)*=a*b* if a,b are quaternions. For same, it is true that (ab)*=b*a*. This result is consistent with the fact that quaternions (eg a = 1w+ix+jy+kz where w,x,y,z are reals) do not commute, b/c in the basis (1,i,j,k) of a quaternion, ij = -ji while ii = -1.

[@joshuablackmon3419]

1:21:30 When he was describing vector spaces of Heads and Tales . You know how 1 vector plus another makes a 3rd vector. I just figured out the 3rd vector of heads and tales ( logically speaking ) the rim of the coin when the coin lands on its rim .. its probability would be low for it to just land and stay on its rim ,but in addition it would be High if the rim just touched the floor and it falls back to heads or tales . That's a interesting idea it almost always lands on the edge of it then falls .

[@thisislizzz]

@fantar132 could you elaborate because susskind is saying that indeed a single particle is affected by the uncertainty principle

[@Dyslexic-Artist-Theory-on-Time]

@hackulous Yes! but when the superposition collapses it will only have one position in space and time. Could this not be a new moment in time as part of the time continuum? Because classical physics is an approximation of quantum physics is it not possible that Heisenberg Uncertainty Principle is the same uncertainty that the observer will have with any future event?

[@inox1ck]

58:35 the inner product of the two function vector spaces looks exactly the same as for ordinary vector spaces. Integral over dx of the functions sums all components over the interval. Instead of φ*(0), φ*(1) .... you have φ*(0), φ*(0+dx) as the next component and so on.

[@schmetterling4477]

Yes, it all looks the same and for the purposes of physics it's basically the same. For mathematicians, however, it's not. There is a lot more (and much darker) "stuff" going on in spaces of functions. If all you are interested in is non-relativistic QM, then you don't have to care about the complications. If you want to know more, then I would suggest you take a class on "functional analysis" in the math department.

[@Sahrinzs]

@jamma246 they need to be orthogonal due to the practicality of not needing to calculate several integrals. He just didn't mention it at this point.

[@haldarin]

@unimoggie Yes, I think it does. We know that alpha h star times alpha h is a positive real. He just stated that probabilities should also be positive reals, so I think it would logically follow that he means the complex conjugate. Also, he hasn't given any other definition of star other than complex conjugation. So why should we assume it has a new meaning.

[@utubewatcher806]

I came for Modern Physics and left with a better understanding of Probability and Statistics..

[@zer0dahero]

Well, delta can mean different things depending on what you are talking about. Obscurusvita told you that delta meant change. In classical physics, some times change is represented by an arrow over the variable and not delta and some times by delta. In the case of this lecture, Delta stands for the undertainty priciple. Go to google or wikipedia and type Uncertainty_principle to get an idea of what delta stands for in this case.

[@kaesspaetzlomator]

It's just the definition of the dot product in that space. As the guy is saying it satisfies the necessary requirements of a dot product. Dot products can be defined differently in all different kinds of spaces.

[@peterpickaxe09]

it would be great if we could hear the questions being asked

[@samferrer]

... more general any Z vector with coefficients in Zn is a vector space ... taking the sum and product as modulus n operations

[@EowYeah]

Thanks for sharing these great classes. Could someone explain how/why we can mathematically consider the dual vector space as the conjugate space ? The way he describes it makes it sounds like it's easily deduced from the definition of a dual space, but for someone like me who has not done mathematics for a while it is not that obvious. (He does not just say that there is a bijection between the conjugate and the dual, but that they are equal)

[@EowYeah]

+Alameen Oredegbe Thank you for your answer, but the dual space here is not identified as a combination of two spaces, but as the conjugate space (that describes the exact same plane, as it, as you stated it, represents the vectors whose imaginary value is opposed). The strict definition of a dual space for a vector space V consists of all linear functionals on V (here V -> C) together with a naturally induced linear structure en.wikipedia.org/wiki/Dual_space so my question was how do you assimilate a dual space defined as this as the conjugate space.

[@markalaverdian1699]

it's not defined that way; there is just an isomorphism between vec.sp. and conj. of dual sp.

[@redotto100]

Hi Adri d, The dual space consists of all linear functionals (V -> C) on the space. In the case of Hilbert spaces, where an inner product is defined, the Riesz Representation theorem shows that the linear functionals in the dual space correspond (isomorphically) to inner products with vectors in the original space. I.E for any linear functional f:V->C, there exists a unique vector v in V such that f(x) = for all x in V. The converse is obviously true since is by definition a linear functional in the variable x on V. source: en.wikipedia.org/wiki/Riesz_representation_theorem

[@EowYeah]

THANK YOU !! (BTW KZbin is displaying your comment -weirdly-, It might be because of your arrows, replacing them by => might work)

[@jjphysstud]

actually, this formulation of quantum mechanics is fairly self-contained. You don't need to do any classical mechanics first. You can do them in either direction. Two different ways of thinking

[@RobotTed]

I would be nice if questions asked were written across the video, since audio of them is unheard. Anyway, goooo Leonard! Quantum the hell out of those Mechanics!

[@Alkis05]

Susskind: "It's just Linear Algebra" Me: "Hum, I clearly remember the linear algebra text book saying that It was talking about just finite dimensional spaces"

[@DumblyDorr]

In a few places, intro linear algebra will say something requires finite dimension - but you can do the same thing in infinite dimensional function spaces if the space is complete (and the norm is induced by an inner product)… Riesz representation for example (finding a vector to represent a linear functional/dual vector via the inner product).

[@xenoepist]

@aaronasterling you are right, I don't think QM can get clearer than this.

[@MrKorrazonCold]

"When waves from the universe enfolds down the spiral vortex of an atom, it will recoil, expanding into three-dimensional spacetime." "The magnetic fields are always enfolding+/-unfolding spacetime at right-angle's." "The symmetry of spacetime is broken where the two waves meet, creating the wobbly particle effect. As these like charged wave-center's repel becoming equally spaced around the spiral vortex, these polarized wave-center's share the same expanding moments of time until acted unpon."

[@kuzuboshii]

1:13:10 so this is sum over instead of sum over i? Is this because vsubi was replaced with the braket?

[@zeperf88]

Don't you know how hard you whacked the electron with the photon? Can't you figure out the electron's velocity before the whack by conservation of momentum?

[@tonix1993]

in 26:30 to satisfie the facts that he tells after , should'nt V1 and V2 be perpendicular to each other?

[@Dyslexic-Artist-Theory-on-Time]

Could Heisenberg Uncertainty Principle be the same uncertainty that the observer will have with any future event? If time and the geometry of spacetime is continuously being formed by the momentum of EMR or light. There is no understanding of time in modern physics or why we have a future and a past. Could this be why we have the paradoxes of QM?

[@ChimpScape]

I fell asleep listening to a Mr Ballen video and woke up with this on

[@tonix1993]

ah sry 1 more thing what you said before means that, a non-independent couple of vectors can create a system. but an independent can create a cartesian?

[@ArjenDijksman]

Nice lecture leading gently into the subject. I miss two things that help to have some intuitive representation of abstract concepts (maybe it will be handled in a later lecture): 1. in the inner product, the ket represents the initial state and the bra the state in which the system ends up (or is projected). Feynman explained that nicely in his introduction to QM. 2. the Argand representation of the complex plane, which helps to visualize the changes of phase in quantum systems.

[@plkarthat]

unable to download these videos i have low bandwidth net connection so i used dap but halfway through it started asking for authentication cant download through itunes either because it doesnt support pause/resume i have slow internet but i want these videos plz help

[@cesarjom]

@floopsie666 if you know how to solve diff eq, (an undergrad physics requirement) then you can solve many problems of the schrodinger eq.

[@cesarjom]

@nementerc... note that a great theoretician does not neccesarily mean you have a great communicator (ie lecturer) particularly to the layperson. Such is the case of Dr Susskind, his insights into his areas of physics are priceless to graduate-level and follow physicists where he can provide much more detailed mathematical arguements... for the layperson there is not much advantage as Susskind lacks the eloquence and succinctness of say a Richard Feynmann.

[@AhmedSabry28]

hey guys how can i find more information about the course, like transcripts, textbook used, lecture notes, assignments, course web page....etc

[@laputahayom]

try going to there site and sarch this lecture.

[@cameronjames7360]

What is the difference between these lectures, and his lectures in Theoretical Minimum: Quantum Mechanics course?

[@samferrer]

Actually the space of boolean vectors is in fact a vector space if it is defined over the boolean field ... it means that the coefficients are also booleans. The only difference is that now product is "and" and sum is "or" ....

[@Travellersfees]

@Mattprole Eucledian geometry is no less difficult, it's just more familiar.

[@avnishbadoni1393]

I kind of feel, that that is actually the case with lots of other things too.

[@fassterblade]

at the risk of sounding slow. if i follow this correctly; it would seem that it would truly be mathematically impossible to violate the uncertainty principle since there would always be a value associated with you looking at the system.

[@tonix1993]

thnx :)

[@jamma246]

@jamma246 Oh, he meant orthnormal basis.

[@cesarjom]

Susskind makes interesting generalizaion: (ab)*=b*a*... this implies non-commutative prop however for a 1-Dim complex a,b this is not true, they do indeed commute and (ab)*=a*b*. It is not until we generalize complex numbers a,b to a higher dim 3-Dim or greater that we run into non-commutative prop. Let a be a quaternion such that a=1w+ix+jy+kz, over a vector space spanned by basis (1,i,j,k) where i,j,k are complex such that ii=jj=kk=-1 and ijk=-1. Only then (ab)*=b*a*.

[@milamber82]

I think this man is only in this dimension part of the time.

[@sivasakthisaravanan4850]

How many lectures are there in total in QM?

[@Dyslexic-Artist-Theory-on-Time]

@QuaterionEM I specifically say we have no understanding of time in physics because we cannot explain why we have a future and a past. We can look back in time through light years of space at the stars. But when we look down at the atom we only see probability. Could this be because Heisenberg Uncertainty Principle is the same uncertainty we have with any future event?

[@albejaine]

An artist theory on the physics of 'Time' as a physical process. Quantum Atom Theory Interesting question.

[@muhammadmohaiminulislam7189]

I would like better picture quality.....Pretty tough to understand.

[@DaveJohnsonsuvam]

run this at 2.0x speed .. and u have a overview of quantum mechanics in just 10hrs .

[@ericbradshaw888]

I just wanted to express my dumfounding thanks for the unbelievable generosity of Leonard Susskind and Stanford University for providing a free Physics education online from who in my opinion is quite genuinely the best physics teacher on the planet... No #Whiteprivilage necessary

[@Slocket712]

You mean by a complex number with i part zero? Yes, that is a real number such as plain number 5 is " 5 + i0 " .the imaginary part is zero. The regular real integer numbers. Vectors are like complex numbers.

[@philoso377]

How much of these help address global warming and CO2 issue?

[@buddhika216]

yup

[@deltro]

all of the forces are the universe abstracting from the 3D matter the 4-dimensional destruction of it. By holographing properties that we observe from particles, we observed that their activity requires 11 dimensions to describe, but it's all meaningless to us, because in reality it's just the completely incomprehensible barrier necessitated by 3 spacial dimensions.

[@maestroanth]

Ugh, that's why I'm so lost, I was watching the entanglements one lol.

[@conman2317]

you can learn any university course you want for free, if you put in time and effort, the DEGREE is what you won't have.

[@conman2317]

I understand that, but the Degree is important, that is if you want to be hired under your particular field. You will not be hired despite your intelect and research over someone who has a Degree.

[@kramarenko]

Briliant!

[@xtremetom180]

nice vid

[@cdaniele87]

I don't understand why he says that in classical mechanics we don't use vectors. We use position and momentum as vectors and we could add for example two position vectors and get just another position vector (the same with forces or fields or other vectors) and we can define inner product (dot product). We can also define a basis for three dimensional space (versors x y z). So I don't really understand what he means when he says that in classical mechanics we use points of a set and in quantum mechanics vectors.

[@markalaverdian1699]

He talks about state of system, in cl. mech. it's just a point in configuration space.

[@r0jter]

I bet you didnt even listen to him. In L1 he made all the distinctions needed to make his point.

[@myclicks]

Why some people insist Susskind should explain "clearly"? QM is not something you can find the analogy from our macroscopic experience. Just get used to it.

[@unnamed6629]

How can something being so fundemental to the existence of things be so asymmetrical? How is there so many questions that cannot be answered through scientificly known theories? There is so much for human kind to learn.

[@43nostromo]

Vector, this is our director.

[@andrew09211]

this is a very interesting subject and id like to learn it. but ts just too long complicated and hard.

[@hasanhelal9474]

I don't know if at 17:12 B is the complex conjugate of A

[@yourmom-nv9ui]

It's just a representation

[@hypatia2001]

I'm getting a message stating that lecture 1 is for private audiences? Is anyone having the same problem?

[@SP-qg4mv]

we never saw michael :(

[@bigdoi814]

How did I get hear, not mad that I am just confused

[@sustaincain]

Nice one. Put up some identity, then we'd be inclined to give you some cool links depending on what you're into. Welcome anyway, its pretty mad out here, but you can learn a lot if you want to. More than one ever dreamt.

[@JumleBumle]

@ICarnag3I Linear Algebra

[@catman8965]

Great video! - learned a little QM. How about "Quantum Coin" rather than "Confused Coin".

[@edyt4125]

16:17

[@026SH]

Good luck, but I recommend to first try to understand some Linear Algebra and Classical Mechanics first. Especially the maths and terminology would make far more sense.

[@666GOREGRINDER666]

I am currently majoring in particle physics actually. I'm starting up quantum mechanics this coming semester. I was just voicing my opinion. Sorry. =/

[@ValMartinIreland]

What I cannot understand is that in a world with so much fantastic mathematics and mathematicians, so many people and their elected governments believe wind energy can contribute to mains electric grids system electric needs. The idea is nuts