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Particle in a Box Part 1: Solving the Schrödinger Equation 

Professor Dave Explains
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Now that we understand the Schrödinger equation, it's time to put it to good use, and solve a quantum problem. Let's find the eigenfunctions and eigenenergies associated with a quantum particle restricted to an infinite square well. This is also known as the famous "Particle in a Box" problem. It's not as hard as it sounds, check it out!
Script by Hèctor Mas
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3 окт 2024

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Комментарии : 204   
@Felixkeeg
@Felixkeeg 4 года назад
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
@shenbagavallia9858 8 месяцев назад
but still i didnt get the ans for my required ques.
@makssachs8914
@makssachs8914 4 месяца назад
Let the particle out of the box!😡😡😡
@matrixate
@matrixate 3 года назад
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.
@zaynabhakim2023
@zaynabhakim2023 3 года назад
You are literally a lifesaver. Perhaps I should send this to my professor.
@keithhammond5501
@keithhammond5501 4 года назад
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
@cafe-tomate 2 года назад
Hey from which university (if it's not lack of discretion)? Je cherche un master également... Cheers
@duck6100
@duck6100 4 года назад
Brings back memories from my undergrad
@benni-1157
@benni-1157 4 года назад
bro
@ivornworrell
@ivornworrell 3 года назад
wow, Lois by now post-covid u-must-b a Math wizz!
@ivornworrell
@ivornworrell 3 года назад
@Lucas Shepherd yea but u gadda 1st no their user name!
@dihydrogenmonoxide6748
@dihydrogenmonoxide6748 3 года назад
@Lucas Shepherd ive seen this comment spammed in every comment there is on existence
@ishaangupta8589
@ishaangupta8589 3 года назад
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
@TheRogueRockhound
@TheRogueRockhound 4 года назад
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.
@지구과학천문학
@지구과학천문학 4 года назад
oh god please tell me this is a series
@ProfessorDaveExplains
@ProfessorDaveExplains 4 года назад
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
@지구과학천문학 4 года назад
@@ProfessorDaveExplains I love you so much...♥
@meleardil
@meleardil 4 года назад
We followed this path in the physics studies... the real satisfaction was when we calculated our first Hydrogen atom and Hydrogen molecule, and the energy levels of electrons. and than we compared it to lab measurements to see, that all that mathematical abstraction were actually representation of something very real and very fundamental. A true "feeling like a god" moment in life.
@frede1905
@frede1905 3 года назад
@@meleardil That's the beauty of physics :)
@ashrafhossain4324
@ashrafhossain4324 2 года назад
@@ProfessorDaveExplains sir can you plz explain : psi=Asin(kx)+Bcos(kx)? How did it come? How to prove?
@pranavlimaye
@pranavlimaye 3 года назад
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
@Ai-ChingChen 3 года назад
Prof Dave is truly amazing!!! It's extremely clear and the steps are well-ordered to let us understand more easily.
@vihaangoel3157
@vihaangoel3157 2 дня назад
Simply lovely! Thanks Professor Dave!
@zhanmaster6733
@zhanmaster6733 16 дней назад
Thank you very much! It became so much plain and understandable after this video.
@light-and-thunder
@light-and-thunder 9 месяцев назад
That was the most comprehensive and well explained solution of the infinite square well problem I ever seen! Thank you Professor Dave!
@codecmac6232
@codecmac6232 11 месяцев назад
how you made this simple is underrated ,you resparked my interest in physics. thumbs up
@charlesnathansmith
@charlesnathansmith 2 года назад
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
@ashrafhossain4324 2 года назад
hi...can you plz explain : psi=Asin(kx)+Bcos(kx)? How did it come? How to prove?
@jhrp1462
@jhrp1462 Год назад
@@ashrafhossain4324 ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-u-ympqH2SBs.html&ab_channel=TheMathSorcerer
@williamcashion5262
@williamcashion5262 10 месяцев назад
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
@tonistar2000
@tonistar2000 4 года назад
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
@ashrafhossain4324 2 года назад
can you plz explain : psi=Asin(kx)+Bcos(kx)? How did it come? How to prove?
@cguy96
@cguy96 4 года назад
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
@mehmethanbuyukdag3245 2 года назад
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
@cguy96 2 года назад
@@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 ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-Dt_VKsSggAo.html Important thing to know is the exponential identity e^(*/-)ix = cos x (+/-) i sin x
@mehmethanbuyukdag3245
@mehmethanbuyukdag3245 2 года назад
@@cguy96 thanks a million Mark :) much appreciated
@jackroche4531
@jackroche4531 Год назад
@@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.
@cliffordwilliams9597
@cliffordwilliams9597 2 года назад
These are my favorite Prof Dave quantum videos...
@emlmm88
@emlmm88 4 года назад
Maaan, I can't tell you how much I wish I'd had your videos back in Pchem.
@stephanietarczynski8608
@stephanietarczynski8608 2 года назад
Great explanation! Sort of understood this in class but now I feel much more comfortable with it. Thank you so much.
@Fatemehsoltani16
@Fatemehsoltani16 4 месяца назад
Perfect as Always, i hoped that you explain how we can find another eigen value (B) for the equation
@0cgw
@0cgw 4 года назад
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
@paulwalker1617 4 года назад
Damn, I'm trying my best to decipher this coded message!
@PrettyMuchPhysics
@PrettyMuchPhysics 4 года назад
Great explanation!
@FeetMyWrathUwU-r8f
@FeetMyWrathUwU-r8f 5 месяцев назад
This has to be one of the smoothest qm video I have seen on youtube.
@biswakumardas8054
@biswakumardas8054 3 года назад
Thank you Professor. You made these things so simple and easier to understand.
@saadhassan9469
@saadhassan9469 2 года назад
Amazing series. People like you are the real heros 👑
@tommyottobisdee
@tommyottobisdee Год назад
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 👍🏼
@takyc7883
@takyc7883 10 месяцев назад
Fantastic video! Far better than any lecture
@yiwang2537
@yiwang2537 3 года назад
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.
@sillypoint2292
@sillypoint2292 4 года назад
I love professor Dave's videos!
@athikhopfoze9761
@athikhopfoze9761 7 месяцев назад
Great explanation.. I'm watching again and again
@AvGeek_ixa2005
@AvGeek_ixa2005 9 месяцев назад
U explained it very simply, Thanks
@utkarshtripathi6777
@utkarshtripathi6777 3 года назад
Really helpful video.....you explain really good at citical point where doubts and confusion can come
@azimmridha8772
@azimmridha8772 Год назад
Thanks dear, You saved my time. Love from Bangladesh 🇧🇩🇧🇩🇧🇩🇧🇩🇧🇩🇧🇩
@daisysmart8874
@daisysmart8874 3 года назад
Thanks for making these videos, they're really helping with my revision!
@kennethhicks2113
@kennethhicks2113 2 года назад
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.
@지구과학천문학
@지구과학천문학 4 года назад
this is the one i was looking for
@OliverHoppe-iy5ly
@OliverHoppe-iy5ly Год назад
Fantastic explanation, very easy to follow along with. Thank you!
@sofiaabidi7607
@sofiaabidi7607 5 месяцев назад
literally bless u. cant thank you enough for all ur help !
@XBJASHITHABATULA
@XBJASHITHABATULA 11 месяцев назад
That was such good explaination
@johnmccrae2932
@johnmccrae2932 4 года назад
Excellent as always
@nadiames8061
@nadiames8061 4 года назад
Thank you for all this useful explanation professor💙
@fettuccine794
@fettuccine794 Год назад
Beautifully explained
@ae5704
@ae5704 2 года назад
Awesome video. Super clear and well explained. Love it
@peterrobinherbert
@peterrobinherbert 3 года назад
The part about the infinite potential always confused me. Nicely explained.
@kall228
@kall228 Год назад
legit, this man is something else
@serenen4630
@serenen4630 7 месяцев назад
This man is the savior. Bout to pass pchem now 🎉
@ZichengYing
@ZichengYing Год назад
AMZING, U are so much better than my professors
@GimbertLane
@GimbertLane 3 года назад
Thank you for creating this series
@havocgaming438
@havocgaming438 14 дней назад
Finally I was able to understand
@DebabrataDutta-by8ik
@DebabrataDutta-by8ik Год назад
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
@nikkicambel1220 4 года назад
i hope a series for differential equations soon! vv nice vids
@Pateckharu3
@Pateckharu3 3 года назад
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.
@imaginaryuniverse632
@imaginaryuniverse632 2 года назад
That's very interesting! I feel certain it's based on the book the Revelation of Jesus Christ to St John from someone who understands that it's all about us individually. The quartz crystal is the new Jerusalem which is a transparent cube with 12 pearl gates. I happened to see on the weather channel a couple of weeks ago how salt cubes are being generated by the dead Sea because it's drying up. I think there is a lot of meaning in the choice of making him a square root symbol. The odds are you think I'm off my rocker but if you are interested check out the last 5 or so pages of the book of the Revelation.. I think the pearly gates relate to our twelve cranial nerves and 12 perfected cell salts as salts seem to automatically seek their perfect match leaving irritant matches for matches that can only be broken in water to loosely paraphrase Walter Russell. Salts are made from the Halogen elements with a metal. I'm sure this is connected to halos, may sound crazy. The river Jordan represents our cerebral spinal fluid which is the river of Life. This river empties into the dead Sea. The 12 cranial nerves flow through and out the Spine in a way I have to say grosses me out a bit because I don't like the look of how this looks like roots coming from a tap root but that is what they are, the roots of the tree of Life. Anyway, don't worry if you aren't interested in what I say for any reason. I am interested if there is anything else you think I might find interesting about that game. 🙏
@Jehannum2000
@Jehannum2000 4 года назад
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
@duck6100 4 года назад
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.
@خربشةإنسان
@خربشةإنسان 7 месяцев назад
Tanks for evry thin in this vid really i can understund some thing
@mohamedhusam8189
@mohamedhusam8189 3 года назад
Amazing video very straight forward derivation and mathematically accurate without being too advanced
@sashaannachemistryconcepts
@sashaannachemistryconcepts 4 года назад
Nice presentation.
@steveying1305
@steveying1305 10 месяцев назад
Low key this video became so useful after I’ve learned differential equations lol
@alicialouv2218
@alicialouv2218 4 года назад
Literally have my first exam today, thank you sooooo much!
@michellehu8264
@michellehu8264 Год назад
Good instruction and explanation
@kiranbhaigaming6462
@kiranbhaigaming6462 Год назад
Awesome. I like the way you explain. ❤
@pritamnath9135
@pritamnath9135 Год назад
Wow it was so well explained! Quantum mechanics is easy if you explain all!
@Meow_yj
@Meow_yj 3 года назад
Thank you, it's helpful !
@matiassantacruz5487
@matiassantacruz5487 2 года назад
Awesome video, helped me a ton. Thank you Professor Dave!!!
@JM-nw5cn
@JM-nw5cn 4 года назад
taking p chem right now, thank you professor Dave
@chakravarthulapriyanka1652
@chakravarthulapriyanka1652 10 месяцев назад
Thank you so much sir
@AbdullahJani-u6k
@AbdullahJani-u6k Год назад
Professor thanks a lot
@coolsammyg47-r
@coolsammyg47-r Месяц назад
Excellent
@kega4062
@kega4062 Год назад
OOOOOOOOHHHHHHHH- so that'ssssssss what my textbook was trying to sayyy
@Jin-ud8ij
@Jin-ud8ij 3 года назад
best QM video ever
@majdiabdalla3505
@majdiabdalla3505 Год назад
Thank you a lot
@juniorcyans2988
@juniorcyans2988 Год назад
Just took a text on this. I wish I could watch it yesterday!
@kochyermo5606
@kochyermo5606 2 года назад
thank you professor dave from ethiopia
@muhepei
@muhepei Год назад
can you explain why the partical has zero probability been outside of the well ?
@alekderijan8348
@alekderijan8348 3 года назад
This was a really nice video. I am 7th grade and I found it very helpful. :)
@drvinylscratch1936
@drvinylscratch1936 3 года назад
ty for the carry for the return to uni. my ability to memorize is bad so this helps a lot
@priyaks6562
@priyaks6562 2 года назад
Thank You Sir
@nisantha6133
@nisantha6133 Год назад
excellent
@bobbudowniczy2496
@bobbudowniczy2496 11 месяцев назад
it is my favourite video
@saviolaaldino
@saviolaaldino 3 года назад
thank you it means a lot to me
@salaheddinesb7312
@salaheddinesb7312 4 года назад
😍😍😍😍😍😍🤗 thank you so much!
@RogerTerrill
@RogerTerrill 3 года назад
Thanks Professor!!!
@5am484
@5am484 2 года назад
I never knew this was so simple
@jinsa.a6760
@jinsa.a6760 3 года назад
Thanks alot... It helped me 😍😍😍
@harshitamahajan1473
@harshitamahajan1473 2 года назад
thankyou
@ButterHaus420
@ButterHaus420 3 года назад
Thanks mate
@pretty.946
@pretty.946 8 месяцев назад
Hi Solve this for me please, For the particle of mass m in the one dimensional box with width a, the wave function of the particle at time (t = 0) inside the box is Ψ(x) = Asin(3πx/2a)cos(πx/2a) 1- Find Ψ(x, t > 0). 2- A measurement is made of the energy. What energies can be found? What is the probability of obtaining each value of the energy?
@ujala6542
@ujala6542 3 года назад
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
@jackhamerordewey9552 Год назад
Please look into “Auxiliary differntial equations”. Luckily, this is one of the easiest types PDEs to solve. Good lick
@juicetime910
@juicetime910 Год назад
finally differential equations make sense
@5am484
@5am484 2 года назад
This is so helpful i wanna cry
@aleezanoor8013
@aleezanoor8013 5 месяцев назад
How can we solve for boundaries x=-a/2 and x=a/2?
@shack1577
@shack1577 3 года назад
well done , Thank you :)
@خربشةإنسان
@خربشةإنسان 7 месяцев назад
حقا أنا جد ضائعة في هاته الوحدة 😢
@qur4334
@qur4334 7 месяцев назад
Aww, 😊 Don't Feel Lost Nor Lonely. You Are Not Ever Alone, Especially If You VOLUNTEER YOUR TIME TO PEOPLE OR THE,🌏🌎🌍🌐⛑️🌊
@خربشةإنسان
@خربشةإنسان 7 месяцев назад
@@qur4334 شكرا، و الحمد لله تمكنت من فهمها و سأسعى لتطوير نفسي من أجل خدمة وطني و العالم إن أتيحت لي الفرصة،
@CB256
@CB256 6 месяцев назад
@bingusiswatching6335
@bingusiswatching6335 2 года назад
Isnt e^ik a solution too? You get -k^2 e^ik + k^2 e^ik which is 0
@pauljackson3491
@pauljackson3491 4 года назад
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
@ProfessorDaveExplains 4 года назад
yep i'll probably cover that a bit later
@RendraNadeViro
@RendraNadeViro 4 года назад
so it is the professor dave will be remembered for roasting flat earthers XD
@ВладСетонов
@ВладСетонов 2 года назад
It seems to me that the quantization only appears because we've defined sin as a periodical function and hence it can be zero infinitely many times. But if we were to define sin only from zero to 2pi for example then we could do the same math and get the same psi function, but this time with n can only be equal 1 or 2. Sooo... I don't really understand this point Sorry for my english btw
@rossfriedman6570
@rossfriedman6570 7 месяцев назад
why is there a time independant form of the Scrodinger equation?
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