Separating the Time Dependent Schrödinger Equation - Hamiltonian, Operators [ Intro to QM #1 ]

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QM Playlist: • Separating the Time De...
Today we introduce the time dependent Schrödinger equation and proceed to separate it into the time independent TISE and the time dependent Energy operator part. We also introduce the notion of the eigenvalue equation being defined wrt a Hamiltonian, which we find analogues to in classical mechanics. Also we "derive" the quantum mechanical momentum operator. Enjoy! =D
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[@michaelg5932]

Looks like papa flammy is playing physicist again xD

[@abcxyz4207]

Technically he’s like two fifth physicist, two fifth mathematician and one fifth didactic stuff because he studied physics and mathematics on Lehramt

[@joeboxter3635]

@@abcxyz4207 His channel is ... maths. How many maths does he know?

[@abcxyz4207]

@@joeboxter3635 two fifth

[@gnikola2013]

1. There's a little observation I'd like to make. When you say that the function identically equal to cero is a trivial solution of the equation you're technically right, if you consider the problem to be simply finding a solution to the equation. However, in the formalism of QM, it's not about just solving Schroedinger's equation, there's another very important condition. The solution has to be square integrable and the integral must yield 1. So, formally, a basic QM problem is not just the diff. eq., but also that the solution should belong to L^2 and integrate 1, aka must be normalizable. This comes from the fact that |psi(x,t)|^2 represents a probability density. So the trivial solution to the equation is not really a valid solution to the overall formal problem. Btw, it can be shown that the chosen normalization is independant of time t. 2. Also, up to what I know, you don't add a hat to E because it is not an operator, it's an eigenvalue of an operator. Kinda like when you write Av = av, you don't really say aight imma set A = a and now a is a matrix. That's not how it works. If anything you multiply the rhs by the identity matrix I and set A - a I = 0. In this QM case, I guess you could set ihdt = E I, with I being an identity operator of sorts, but E itself ain't an operator, E is an eigenvalue of H^.

[@bairrao1303]

@Robin Hack The "hydrogen atom problem" as usually presented is about finding the wave function for the electron, the proton's influence is simply the Coulomb form for the potential. The trivial solution really has nothing to do with the proton because it is simply treated a a "background" potential influencing the dynamics of the electron. I guess you can look for a more realistic model in which the dynamics of the proton are taken into consideration and the wave function describes both particles, and then look for a solution in which the electron is not there, but that will not be the trivial solution.

[@mudkip_btw]

Sometimes the Hamiltonian is not equal to the total energy (remember classical mechanics), in which case an E operator could make sense. But a bit far out there though in terms of practical problems

[@gnikola2013]

@Robin Hack hmm I guess so, the trivial solution would be the lack of a particle, but I think we can agree that if there's no particle, there's not really something to study at all

[@axemenace6637]

@@gnikola2013 the actual formulation for the problem we want to solve is, "where can the electron in a hydrogen atom be located"? The formulation of the problems necessarily requires that the probability that the electron is located SOMEWHERE is equal to 1, so we can't say that the trivial solution is when there is no electron (because that contradicts the assumptions of the problem).

[@Harkmagic]

That was actually much easier to follow than my quantum physics course.

[@johnnymccougar2526]

I presume it's because like in my case, the guy teaching it doesn't know how to teach it and just copies what's in a book?

[@hasan7275]

it's my birthday today and i gotta say this vid is the gift i appreciate the most.

[@PapaFlammy69]

awwwww

[@h4z4rd28]

First episode: measuring the speed of light with chocolate! Second episode: Separating the time dependent Schroedinger equation!

[@pabloxd4673]

Third episode: Quantum gravity

[@h4z4rd28]

Fourth episode: Theory of everything +BONUS solving riemann hypothesis

[@pabloxd4673]

Five episode : Solving Navier-Stokes equations in quantum curved space-time with basement boundary conditions

[@h4z4rd28]

@@pabloxd4673 but you forget that he will be doing it as a speedrun

[@joda7697]

Sixth episode: Integration chain rule because why not at that point.

[@dozzco2827]

This is going to be the Best Series In the Two-Torus House!

[@erikawimmer7908]

Ooooooo yeah

[@suppeoples21]

Papa talking about units??? 2020 is crazy

[@CrittingOut]

So the plan all along was to: Capture scientists, Force them into your basement, Feed them nutritious dust, Have them teach you their field, Become ultimate stem amalgamation and take over youtube?

[@nimrodboshilevine9685]

Just like college!

[@Akira-shakira]

It’s a nice refreshing feeling to revise how to separate partial differential equations and taking a little break seeing non relativistic quantum mechanics after staring at a Klein-Gordon Lagrangian for a whole day

[@mastershooter64]

2 days ago i was like "bruh i dont understand this" but now im like "oh the time independent schrodinger equation!" dark matter is one hell of a drug

[@frozenmoon998]

Papa Flammy: *Uses cool intro* Also Papa Flammy: *Wrong channel*

[@alexandergoldthorpe4585]

Yes! The TISE and TDSE in 1D, 3D, and spherical coordinates, eigenstates, commutable operators, hydrogen atom and SHO will be coming up in my January exams for Quantum Mech. This is a big help! Thank you :))

[@lc7269]

I just got my flammable maths engineering clock by mail today! Absolutely love it!

[@m_riatik]

i'm actually doing a semiconductor physics course rn which has a QM part and i have to say, this is the most in depth explanation of separating the Schrödinger equation i've ever seen. looking forward to more!!!

[@emanuelvendramini2045]

The most interesting of all it is that the time dependent function eta(t) is a composition of waves (like a sum of any e^wt where w is a complex number).

[@PapaFlammy69]

:)

[@epicmorphism2240]

Hi papa flammy! First of a all I am going to buy the iPad. It looks very comfortable to write on. I also wanted to say that I am more into theoretical mathematics but I am thinking about going in to theoretical quantum-physics. So I will enjoy this Video surely. Lastly I wanted to think you again for showing me the Desmos graphs! Right now I have to draw the most complex contour I have ever drawn haha! Have a nice day and don’t forget to bring Andrew food!

[@PapaFlammy69]

Good stuff Daniel! Glad the graphing is working out :)

[@WWLinkMasterX]

My quantum professor gave us this same lecture a couple years ago and I had forgot the details. Very nice coincidence that you uploaded this only two days ago.

[@LeoxandarMagnus]

Ah, I love the smell of Hamiltonians in the morning *Junior-year QM flashbacks intensify*

[@sapphirezephyr5050]

Wow, one day before my QM final exam, thanks papa flammy!

[@genessab]

Wow I’ve actually been struggling with this this quarter thank u flammy boi

[@ironheadrondo5596]

I like vector notation. I see how with a cirtian amount of understanding you don't need them, but I like a simple arrow over vectors, it's a very common notation and would make it easier to understand.

[@davidlenir7517]

You should really consider starting with two-state systems and Bra ket notation. The TDSP is a lot more intuitive when analyzed without projecting into any particular representation (Like position in your case).

[@imranq9241]

Finally physics, doing something that’s not “trivial”

[@jameshills6076]

Papa teaching qm is so chill 🤤

[@krishnasimha8097]

QM series freaking awesome 😆😆😆😆

[@allbums7038]

I am very excited for this series

[@sherlockholmes1417]

This was an ingenious video! Thanks, Papa to make videos more about physics , because physics it's math apply to the real world

[@user-pc9bd9cf2o]

gonna love these series papa

[@tylerfusco7495]

YES LETS GOOO

[@jamesbra4410]

that board smacks

[@thekinghass]

Finally papa doing some physics

[@seandimmock5813]

I like the format, it’s just as, if not more, easy to follow and understand than black board videos. However I have been looking for an explanation of quantum mechanics as an infinite vector (hilbert) space and the derivation of wave function properties and operators etc. Not sure what you’re background is on linear algebra, but being the worlds best mathematician I’m sure it’s pretty good, just wondering if you would be able to explain some of that. Anyway, love the video.

[@HAL-oj4jb]

21:17 isn't the reason for that because the energy E is the eigenvalue of the hamilton operator? If i remember correctly H was always the operator, and E just a value and not an operator

[@compphysgeek]

yeah, E on the right hand side is the Energy eigenvalue and doesnt get a hat, but iħðt on the left hand side is the Energy operator and should get a hat on and most of the time I have seen it it did have a hat

[@3manthing]

So the only "drawback" the new Gaomom tablet has, compared to the old one is, that it's to big... Real bummer.

[@PapaFlammy69]

A bit, yes ^^

[@Happy_Abe]

“Reminder” As if I knew that before lol

[@krishnasimha8097]

Flammable physics

[@cleo7363]

I want more now 🙂

[@mudkip_btw]

Series on qm heck yeah

[@mudkip_btw]

U should do electrodynamics at some point

[@mudkip_btw]

Seen as you said you were confused why physicists don't really put a hat on E: In some situations, the Hamiltonian is not equal to the total energy of the system (particularly in non-intertial reference frames iirc). In this case, E would be written as an operator. The Hamiltonian is defined by the Lagrangian, which is exactly K - U (kinetic - potential energy). The fact that E is the eigenvalue does not disqualify the letter E from being an operator, since x^ is also an operator with eigenvalues x' for eigenstates |x'> = delta(x-x'). However, since usually H = E, H^ makes writing E^ unnecessary, since H^ is a well defined way of calculating the energy in general (from position, momentum, and potential). Hope that was clear

[@Juan_Carl0s]

What? It's a simple matrix equation (because the symbols are capitalized), so it gets back to the homogeneous equation (H-E)PSI=0. Either PSI=null(H-E) if det(H-E)=0 or the vector PSI has the trivial solution 0.

[@ryans7536]

Good video!!

[@phyarth8082]

I watched this video and wave function collapse by observing and by changing the final result of this video and innocent cat in the box is dead :)

[@FGj-xj7rd]

Papa Schrodinger would be very proud.

[@duncanw9901]

Perhaps instead of saying you're not factoring out the operator every time you could say that you're factoring it out in the sense of the operator algebra over functions on R

[@PapaFlammy69]

That makes more sense, thanks Duncan! =)

[@tp_2301]

5:33 When you see its physics

[@rabiajoubran9107]

Thanks for the video, is there more videos about quantum physics

[@exequiellopez4024]

Lovely. I had this topic in my first test of my Chemistry PhD and I liked a lot. And yes, I am a metallurgical engineer.

[@ahmedsaadsabit1749]

I love the way he says "FAkin kuul"

[@brendawilliams8062]

Why does mass motion and energy give you a total energy. And then in comes velocity with a potential energy. Does 2 pi actually give you a potential.

[@benthayermath]

Grandpapa Schrödinger

[@meenu5910]

Hello sir I am from India

[@BadassRaiden]

Can someone tell me what are good prerequisite for QM? Also would love to know if Understanding Physics by Issac Asamov is a good for a basic foundation? Obviously we've come a long way since then, but its the only like full volume physics book i have (it contains all three volumes of his in fact), and was given to my by a friend's grandparents.

[@mynamehere69]

I would love more on intro to QM, my current professor at university doesn't like griffeths at all and we never got past chapter 3, he spent all semester going on about topics about chapter 1, and 2 and didn't cover anything. I would Really love more of these vids, so I can prepare my self for next semester!

[@VaradMahashabde]

Papa if you are quick you can overtake @LetsSolveMathProblems

[@PapaFlammy69]

What do you mean? My second channel?

[@CrittingOut]

Wait where is the donauwelle tho = )

[@trishanmondal7813]

I must say i miss the chalk and board because somehow i feel they are much much suitable for papa flammy ;)

[@1976kanthi]

Papa Flammy! :3

[@zer0day463]

He's a gamer ... No he's a Teacher 😂😂

[@SomeGuy-pc9fh]

Who also doesn’t even do maths or physics and is still watching this video

[@ChrisChoi123]

i wanna buy the tablet for drawing anime tid-- err, i mean doing quantum mechanics. yes, definitely doing quantum mechanics.

[@joeboxter3635]

Please can you count all the maths? How many maths are there?

[@ricardoparada5375]

I agree with the meme lmao

[@PapaFlammy69]

:D

[@darvinong4621]

Is that only me who just noticed the mouse padXD?

[@provki]

which software do you use on the tablet?

[@PapaFlammy69]

Windows Ink Whiteboard =)

[@provki]

@@PapaFlammy69 thanks ❤

[@T3WI]

Won’t your basement gremlin get mad at you for doing this?

[@PapaFlammy69]

he quantum tunneling-ed into my chocolate cave, so that's dealt with

[@AndrewDotsonvideos]

@@PapaFlammy69 phrasing

[@PapaFlammy69]

yeye

[@kshitijsalunke2620]

you made 2 videos about physics continuously I don't think your intentions are right.

[@joyboricua3721]

When you say "right here" but there's no cursor to follow... Imma sleep now anyway. Tomorrow then

[@PapaFlammy69]

need to work on the presentation a bit hehe :'D

[@jperez7893]

can you please derive / prove the noether's laws

[@crystal_royal3405]

Wow

[@legendarysom5605]

hi dad pls react on John gabriel new calculus and make the video PLEASEEEE SEE THE COMMENT

[@limerence18]

I lost it at "die in hell" :D

[@rhealastname266]

Good meme

[@goesgallucci-advogados5530]

Lmao, wrong channel

[@mairisberzins8677]

The handwriting is easier to understand on this drawing tablet than a chalkboard. No offence to the chalk.

[@abcxyz4207]

Where is that black blue Mandelbrot pic from I need it

[@PapaFlammy69]

All the merch available over on STEMerch :) stemerch.com/collections/mandelbrot It's the Canvas Print!

[@abcxyz4207]

@@PapaFlammy69 very expensive :(

[@PapaFlammy69]

But the quality is really superb =)

[@abcxyz4207]

@@PapaFlammy69 + 6$ shipping though 😅

[@TheMercury79]

I have liked and enjoyed many Flammable Maths videos but this time I felt like I literally walked into a shop and a store clerk rushing towards me trying to sell things. I didn't mind when it was just t-shirts but now the Flammable Maths chanel has expanded into a souvenir shop of "fun maths items" for teenagers who think they really need this stuff to do mathemathics. It was better when you stood in front of the board with a good old white chalk, this screen thing you were using here just felt disconnected and I rather just look for solutions to the Schrodinger Eq. in a quantum mechanics book than watching this commercial drivel

[@torment808]

black methamagic

[@sharpfang]

Laughs at engineers for using j. Applies square root to 2nd derivative to get 1st derivative.

[@NikolajKuntner]

nothing but

[@retaliatorliteratora]

Hey, i'm 'fast', but i don't know 'where' i am now.

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Hello there :v

[@blackhole3407]

Me whos still learning about similar triangles at school: 😐

[@pablodominguez526]

Beautiful title lmfao

[@user-ps1dm4fc4l]

ايلافيوه (:

[@daveconerly1450]

Your not andrew dotson. Why you clap your hands and say whats going on smart people , although you left out smart ? Are you giving over to his channel as being better than your own ??? You know that's the problem with intermingling with another math station. You help them with enforcement's, you blend by helping them out in referring to more inquest with same like topic, then it all explodes. Now people are going to andrews channel and leaving you to pick up the pieces. Fellow mathematicians are physics people now. You have started the trend. Flammy must start giving big prizes like big million dollar money to keep people on his channel. Shard the money your making and share the love with putting big money into the struggling maths professions pocket. All your devices , clothes etc are under the gold and hold of you flammy , the CEO and founder of that crazy guy with all the fun equations.

[@mechwarreir2]

a mathematician..... NOT USING CHALK!??? What is this blasphemy.

[@gr00veh0lmes]

STOP SWEARING

[@crystal_royal3405]

Not first

[@nathannguyen2041]

This is faker than COVID-19. All you're doing is moving symbols around and you call yourself "smart" . I kid, ples no murder me ;-;