Particle in a Box Part 1: Solving the Schrödinger Equation

[@itzprac]

I am an btech undergrad from India and chemistry was there in my 1 semester which was a headache to me as there are no such descriptive videos for it, U turned out to be a life saviour, thank you very much😊

[@Felixkeeg]

Man, this brings back memories. This was one of the more satisfying things to do. Things being equal to zero and canceling out and ultimately arriving at a very clean solution is nice.

[@shenbagavallia9858]

but still i didnt get the ans for my required ques.

[@makssachs8914]

Let the particle out of the box!😡😡😡

[@reaox7917]

free my man particle he did nothing wrong

[@allbookshorts1025]

Which kind of differential equation it is partial second order or normal

[@zaynabhakim2023]

You are literally a lifesaver. Perhaps I should send this to my professor.

[@TheRogueRockhound]

Not afraid to admit I need to go back to less advanced videos. Thanks for taking the time to make these, I hope to purchase a mug or something in the near future.

[@ishaangupta8589]

Man I couldn't understand anything from the slides I had , and all that maths was frightening. Thanks to you I am confident enough to try this by myself again. You are doing a great work please keep it up

[@keithhammond5501]

I'll be starting my second quantum chemistry course in a few days, that was very helpful and couldn't have come at a better time. Thank you Professor Dave you rock as usual! Kudos from France

[@cafe-tomate]

Hey from which university (if it's not lack of discretion)? Je cherche un master également... Cheers

[@matrixate]

I have to say...this is definitely well-scripted. Clearly, you've included the best parts of other videos and put it all together in one succinct, clear, and concise presentation. Honestly, it's about time someone did this. Thanks for making this available for everyone. I wish I would have had this when I took QM. It's all good...I had a lot of smart friends and grad students that were around to help clear things up.

[@pranavlimaye]

I missed a whole bunch of physics lectures because of medical reasons. *I've never been more glad to be your subscriber....* Thanks Professor Dave!

[@Ai-ChingChen]

Prof Dave is truly amazing!!! It's extremely clear and the steps are well-ordered to let us understand more easily.

[@지구과학천문학]

oh god please tell me this is a series

[@ProfessorDaveExplains]

yes check the modern physics playlist, the last 4 i've posted have been part of this miniseries on a more rigorous approach to quantum mechanics

[@지구과학천문학]

@@ProfessorDaveExplains I love you so much...♥

[@frede1905]

@@meleardil That's the beauty of physics :)

[@ashrafhossain4324]

@@ProfessorDaveExplains sir can you plz explain : psi=Asin(kx)+Bcos(kx)? How did it come? How to prove?

[@jackhamerordewey9552]

@@ashrafhossain4324 its a differential equation that you have to solve. Differential equations are very different than regular problems. It involved using ansatz aka guessing

[@duck6100]

Brings back memories from my undergrad

[@benni-1157]

bro

[@ivornworrell]

wow, Lois by now post-covid u-must-b a Math wizz!

[@ivornworrell]

@Lucas Shepherd yea but u gadda 1st no their user name!

[@dihydrogenmonoxide6748]

@Lucas Shepherd ive seen this comment spammed in every comment there is on existence

[@codecmac6232]

how you made this simple is underrated ,you resparked my interest in physics. thumbs up

[@williamcashion5262]

I've been looking at this and similar videos for maybe 6 years. Including the MIT series. Something about the way you presented this, I suddenly realized the integers ñ=2 ,n=3, etc, yielded the outer orbits. Thank you. Bill

[@cguy96]

I would like to point out that the entire equation could be solved strictly mathematically, and it really isn’t that difficult. I assume Dave is quite capable of doing this. However, the way he used, by looking at how the terms look and behave is much more useful to someone learning it, because it helps you to visualize it. If you just went ahead and solved it, there are multiple places that errors could have crept in, and you would have no idea, ecause you would have no appreciation for what you were looking for. Nice job!

[@mehmethanbuyukdag3245]

Is there a link that solves it step by step, im a chemistru student and i do not have a clue how psi = a sin (kx) and B sin (kx) , every single video just assumes thats the baseline

[@cguy96]

@@mehmethanbuyukdag3245 there are, but this setup gives a fairly simple PDE that can be separated into x and t equations, and then transforms to an ODE. You may not get much from a step by step if you have little to no PDE (and ODE) experience. Here is one that will carry you much of the way kzbin.info/www/bejne/eqXCh36piMyad9E Important thing to know is the exponential identity e^(*/-)ix = cos x (+/-) i sin x

[@mehmethanbuyukdag3245]

@@cguy96 thanks a million Mark :) much appreciated

[@jackroche4531]

@@mehmethanbuyukdag3245 The wave equation is just a 2nd order homogenous linear partial differential equation ( I know that sounds insanely complex but its not as bad as it sounds) . This differential equation can be solved by using the "characteristic" equation method. It just requires subbing e^(rt) in for Psi ( you will see in doing differential equations how incredibly useful Eulers constant and Eulers formula is). Subbing this in, and doing the derivatives leaves you with a quadratic, where you may simply find the roots, and plug them into the characteristic formula. You will get complex roots and using Eulers identity (e^(ix)=cosx+isinx). After some algebraic manipulation, and dropping the "i" term (which you may do because the solution is a real value solution), you will eventually arive at Asin(x)+Bsin(x), then just plug in the proper variables.

[@0cgw]

Great video. You can prove that E≥0 and hence k is real by using that E= = /2m + ≥ ≥ min V(x) =0. "If E=0 we don't even have a particle to begin with" Huh??? That rather depends on the potential. Just as in classical theory, if the potential energy is negative (admittedly not the case here), then E=0 is possible (e.g., parabolic orbits). You should rule out E=0 by the boundary conditions at x=0 and x=a (or show E=0 implies that ==0 and =0 implies that ψ=0.) The quick way of getting the normalization is to remember that the average value of sin²(x) over an non-zero integer multiple of the half period is ½, Thus = ½(length of interval)= ½a. Obviously, the reason why this works comes from the trig identity you quoted. This result is also useful when playing around with Fourier series.

[@paulwalker1617]

Damn, I'm trying my best to decipher this coded message!

[@tonistar2000]

Thank you so much ! This is exactly what I am studying right now, and you make everything so much clearer and easier! Keep it up! I am waiting for your future videos of the series. :)

[@ashrafhossain4324]

can you plz explain : psi=Asin(kx)+Bcos(kx)? How did it come? How to prove?

[@tommyottobisdee]

I’m staggered by how much clearer this is to understand than my university textbooks?! If only I could find a book that explains all of QM so clearly I’d have my module done in a few weeks, honestly! I notice others have commented on how disarmingly simple the maths methods ultimately are here, and I’m inclined to agree… However, there are so many sudden leaps from one equation to another, seemingly, on a whim in this topic - dividing by i, BUT being expected to use (-i), instead of 1/i, is a good example - that, if the situation just isn’t explained well, it gets baffling fast! Thanks so much, easy sub from me 👍🏼

[@light-and-thunder]

That was the most comprehensive and well explained solution of the infinite square well problem I ever seen! Thank you Professor Dave!

[@emlmm88]

Maaan, I can't tell you how much I wish I'd had your videos back in Pchem.

[@joserobertopacheco298]

This is a magnificent explanation. Thank you for your time, Professor Dave

[@charlesnathansmith]

This supplements the MIT OpenCourseware series really well. Both are great, but seeing the math broken down from a couple of different angles is really helpful

[@ashrafhossain4324]

hi...can you plz explain : psi=Asin(kx)+Bcos(kx)? How did it come? How to prove?

[@jhrp1462]

@@ashrafhossain4324 kzbin.info/www/bejne/q17cnqOnfZeGeNU&ab_channel=TheMathSorcerer

[@cliffordwilliams9597]

These are my favorite Prof Dave quantum videos...

[@saadhassan9469]

Amazing series. People like you are the real heros 👑

[@PrettyMuchPhysics]

Great explanation!

[@stephanietarczynski8608]

Great explanation! Sort of understood this in class but now I feel much more comfortable with it. Thank you so much.

[@biswakumardas8054]

Thank you Professor. You made these things so simple and easier to understand.

[@takyc7883]

Fantastic video! Far better than any lecture

[@sillypoint2292]

I love professor Dave's videos!

[@FeetMyWrathUwU-r8f]

This has to be one of the smoothest qm video I have seen on youtube.

[@vihaangoel3157]

Simply lovely! Thanks Professor Dave!

[@zhanmaster6733]

Thank you very much! It became so much plain and understandable after this video.

[@azimmridha8772]

Thanks dear, You saved my time. Love from Bangladesh 🇧🇩🇧🇩🇧🇩🇧🇩🇧🇩🇧🇩

[@yiwang2537]

Thank you so much, really save my life , my prof explain quantum in an sleepy way. Watch your video, I even don't have to pause and think.

[@daisysmart8874]

Thanks for making these videos, they're really helping with my revision!

[@aditya_asundi]

Wow! Such clear explanation. I have my physics final tomorrow, hope I am able to pass, at the very least. Thank you!

[@Pateckharu3]

Your videos are very good and easy to understand. Ive seen those concepts so many time but without knowing maths and equations... Its so fascinating. in super mario rpg world, there is that interpretation of matter and antimatter, see past, present and future, consuming time and consuming you. you defeat it fair and square then you get reward quartz charm in a crystal form giving you immunity to the quantum of the world. kind of... it's AI is based on calculation and what is the best action possible for any turn based... he looks like the root square symbol too hahah. wow Im blown away.

[@kennethhicks2113]

Been watching the whole series, I have to say great job, sub'ed. And on the topic, this is all that's really required to explain virtual particles. But it all breaks when "a" < Planck length.

[@kall228]

legit, this man is something else

[@utkarshtripathi6777]

Really helpful video.....you explain really good at citical point where doubts and confusion can come

[@지구과학천문학]

this is the one i was looking for

[@athikhopfoze9761]

Great explanation.. I'm watching again and again

[@serenen4630]

This man is the savior. Bout to pass pchem now 🎉

[@AvGeek_IXA]

U explained it very simply, Thanks

[@Fatemehsoltani16]

Perfect as Always, i hoped that you explain how we can find another eigen value (B) for the equation

[@GimbertLane]

Thank you for creating this series

[@nadiames8061]

Thank you for all this useful explanation professor💙

[@johnmccrae2932]

Excellent as always

[@OliverHoppe-iy5ly]

Fantastic explanation, very easy to follow along with. Thank you!

[@kiranbhaigaming6462]

Awesome. I like the way you explain. ❤

[@muhepei]

can you explain why the partical has zero probability been outside of the well ?

[@SasukeUchiha-e3t]

As we know that in any force field, any kind of particle tends to move from higher potential to lower potential. So there's higher chance of finding the particle somewhere at the lower potential. That's what's going on here. V=1/0 is high potential and V=0 is the low one. So where do you expect to find the particle at?

[@AnonymousBoy_764]

Beautifully explained

[@sofiaabidi7607]

literally bless u. cant thank you enough for all ur help !

[@peterrobinherbert]

The part about the infinite potential always confused me. Nicely explained.

[@riskant8263]

incredibly clear. thanks

[@ae5704]

Awesome video. Super clear and well explained. Love it

[@ZichengYing]

AMZING, U are so much better than my professors

[@Marina-rm9vz]

Thanks! This is so helpful!

[@salaheddinesb7312]

😍😍😍😍😍😍🤗 thank you so much!

[@DebabrataDutta-by8ik]

Very organised and Good explanation Of concepts Appreciate the effort I came when I didn't understand a Topic In My paid Course for IITJAM

[@nikkicambel1220]

i hope a series for differential equations soon! vv nice vids

[@yukthiabhinav2152]

This is same explanation I got in physics class but here I understood far better

[@خربشةإنسان]

حقا أنا جد ضائعة في هاته الوحدة 😢

[@qur4334]

Aww, 😊 Don't Feel Lost Nor Lonely. You Are Not Ever Alone, Especially If You VOLUNTEER YOUR TIME TO PEOPLE OR THE,🌏🌎🌍🌐⛑️🌊

[@خربشةإنسان]

@@qur4334 شكرا، و الحمد لله تمكنت من فهمها و سأسعى لتطوير نفسي من أجل خدمة وطني و العالم إن أتيحت لي الفرصة،

[@CB256]

❤

[@mohamedhusam8189]

Amazing video very straight forward derivation and mathematically accurate without being too advanced

[@alicialouv2218]

Literally have my first exam today, thank you sooooo much!

[@matiassantacruz5487]

Awesome video, helped me a ton. Thank you Professor Dave!!!

[@Jehannum2000]

I look forward to the tutorial on the physical implications of this situation. I'm realising that once you've got the maths down, it's beneficial - and enjoyable - to think through what the maths is telling you. This is how you develop intuition that might help in more difficult problems.

[@duck6100]

You'd probably want to watch a video on finite potential wells and quantum tunnelling then. There's not much real life in a infinite square well.

[@kega4062]

OOOOOOOOHHHHHHHH- so that'ssssssss what my textbook was trying to sayyy

[@sashaannachemistryconcepts]

Nice presentation.

[@michellehu8264]

Good instruction and explanation

[@pritamnath9135]

Wow it was so well explained! Quantum mechanics is easy if you explain all!

[@JM-nw5cn]

taking p chem right now, thank you professor Dave

[@XBJASHITHABATULA]

That was such good explaination

[@Jin-ud8ij]

best QM video ever

[@Meow_yj]

Thank you, it's helpful !

[@jinsa.a6760]

Thanks alot... It helped me 😍😍😍

[@alekderijan8348]

This was a really nice video. I am 7th grade and I found it very helpful. :)

[@kochyermo5606]

thank you professor dave from ethiopia

[@خربشةإنسان]

Tanks for evry thin in this vid really i can understund some thing

[@steveying1305]

Low key this video became so useful after I’ve learned differential equations lol

[@havocgaming438]

Finally I was able to understand

[@chakravarthulapriyanka1652]

Thank you so much sir

[@RendraNadeViro]

so it is the professor dave will be remembered for roasting flat earthers XD

[@drvinylscratch1936]

ty for the carry for the return to uni. my ability to memorize is bad so this helps a lot

[@HarshilKapadiya-ii9gp]

Can anybody write the subtitles of first 5 seconds..... I didn't get that initial part....

[@MichelleTogbe-d5o]

TY SM explained better than my pchem teacher

[@gamerspoint4256]

Can I get notes of this

[@AbdullahJani-u6k]

Professor thanks a lot

[@RogerTerrill]

Thanks Professor!!!

[@pauljackson3491]

Are you going to, or did you, make a video on quantum tunneling with the math involved? Maybe how it allows transistors and fusion (apparently gravity and heat isn't enough) to work.

[@ProfessorDaveExplains]

yep i'll probably cover that a bit later

[@priyaks6562]

Thank You Sir

[@ujala6542]

Can you please explain the mathematical procedure to solve the equation (d2¥/dx2) + k.k¥ =0 Or please give me the resources where the whole thing is explained instead of hit and trial method

[@jackhamerordewey9552]

Please look into “Auxiliary differntial equations”. Luckily, this is one of the easiest types PDEs to solve. Good lick

[@coolsammyg47-r]

Excellent

[@saviolaaldino]

thank you it means a lot to me

[@majdiabdalla3505]

Thank you a lot

[@bingusiswatching6335]

Isnt e^ik a solution too? You get -k^2 e^ik + k^2 e^ik which is 0

[@juniorcyans2988]

Just took a text on this. I wish I could watch it yesterday!

[@Shivally6]

Being 7tj grade I don't understand a still fucking thing in here😂(dream to become science student 😅)

[@s1nd3rr0z3]

This video is a bit old, but I've been curious for a while as to where your videos on differential equations are. Were you planning on making them and haven't done that yet, or were they hidden/deleted for some reason?

[@ProfessorDaveExplains]

haven't managed to do it yet sadly

[@s1nd3rr0z3]

​@@ProfessorDaveExplains Oh, that's disappointing as your math videos have been very helpful when I'm studying before taking a class, and I'm going to be taking ODEs not too far in the future. I also just wanted to thank you, as before I found your mathematics playlist I was struggling to relearn HS algebra, but I'm now having a pretty easy time in calculus and am planning on majoring in mathematics. So do please know that you're having a very direct positive impact on the education of a huge amount of people 💜.

[@rossfriedman6570]

why is there a time independant form of the Scrodinger equation?