Infinite square well (particle in a box) 

Such a wonderful video. Thank you for making it so easy to re-familiarize myself with what I learned ages ago!

"The infinite square well is called that because it's potential is infinite... and, well.. square" I see what you did there ;) Plus a good explanation, thanks!

The answer to the final question is the following (i think) : Solving the TIDSE does NOT give you the Wavefunction Ψ(χ,t) , but X(x). The Wavefunction will therefore be Ψ(χ,t)=Asin(ka)e^(-iE/hbar)t , which of course is a complex function.

Thanks for the video. I have struggled with Schrodinger's equation for years but you have explained it very well.

Brant - PLEASE write a Modern Physics text book on this stuff! Your presentation is perfectly clear at all times, the modern physics text by Krane on this is horrible in comparison.

Thank you. This was a super helpful review. My Stat-Mech professor brought up particle in a box today and I completely forgot everything except that it was a particle in an infinite square well.

Such a good video! you explained the concepts very well. Thank you so much!

Thank you! Keep doing what you're doing!

So i was trying to find a video that explains infinite square well clearly, and this is the one i found! Extremely clear explanation, precise and beautifully presented, thank you so much for this video. I do want to point out, for those who get confused while watching the video, that at 17:15 there is a typo, the E should be replaced with E^2. Anyways, great video and i hope you keep doing videos like this to help others.

Wonderful walkthrough. Thanks! :-D

Great video! Helps a lot!

I study theoretical physics and this is so helpful for my midterm thank you omg ❤

you sound like Eric from That 70's Show

Mr. Carlson is awesome thanks so much for these videos

Very clear and definitive. Much easier to understand than my textbook. Thank you.

you did a great job explanation the equation

you are a virtuoso at melding mathematical models with real like examples and diagrams, ty sir

Wow, well done and explained.

Thank you! Very helpful video!!

Thank you very much. ALL your presentations are very clear and helpful. Do you have presentation on electro dynamic Jackson as well? Thank youuu!!!

I am watching this vedio in 2020 during Corona virus pandemic to improve my self in quantum physics and its realy very good with detailed explanation that help understand the subject thoroughly

thank you so much for that awesome video .. i undersood the exercice very well

thx alot mr brant , your vid was very helpful

Very nice Tutorial man...

Thank you! You are a life saver.

This is great!

Thank you ! For the questions at the end: 1- I still did not get the relation between the infinite V(x) and the second spacial derivative of the wave function..why does the question assume that an infinite V(x) implies an infinite second spacial derivative of the wave function? 2- Complex numbers indeed include real numbers, so we are not breaking a QM postulate. More importantly, we can expand the exponential solution in terms of sin and cos, and continue solving using the boundary conditions and we will end up with our solution! Also, we assumed the solution of sin and cos due to the formula that resembles a simple harmonic motion that we got when we substituted with our conditions, and that can be expressed also exponentially, so our action is driven by a reason and does not contradict a postulate.

thank you so much for this

You are an amazing person sir

Excellent exposition

Nicely explained

Thank you you helped me alot

Thank you for nice explanation. One thing I'm struck with, what really is or difference between single well and Double well potential. why do we need double well potential when we already have Single well potential well solution?? Any help.

You are awesome man 👍👍👍👍

what is an amazing way thank you alot

SO CLEAR> THANKS SO MUCH!!!!

thank you so much

U r the man!!!!

For the first one the second derivative cannot be evaluated at x=0 or a because it is not smooth (it is continuous, but not smooth). The second one: The solution in general is complex, but it does not have to be. Another issue is that you could not use the coefficients A and B with it since it is one term, and it could not be set for the boundary conditions correctly. These are my guesses.

Is there such kind of lucid teaching videos on other topics( Like- relativity, Quantum field theory,)?

For the questions my take is: 1. All wavefunctions drawn at the end, end on the axes (regardless of whether odd or even). In the previous video it was stated that if V(x) > E which outside the bounds is cause infinity, it would move away from the axes, unless it was stuck on the axes. In this example, it is stuck on the axes so it cannot leave towards infinity and is stuck at 0. 2. Wavefunction is complex, but the solution gotten at the end of this video, is only the spatial part. The complete wavefunction adds the time evolution as well, which is a complex exponential, hence we have not broken any features of QM. Another take on 2 could be that this spatial part could be considered complex, but with an imaginary term 0i.

1) dψ/dx is continuous except at points where the potential is infinite. A particle outside the well would have infinite energy. Since is impossible to find the particle outside that boundary, we must have |ψ|²=0 in this region. ψ is always continuous. This brings us to the boundary conditions ψ(0)=ψ(a)=0. 2) Considering all possible Schrodinger equations, ψ is in general complex. But that doesn't mean that for any particular case we will encounter a complex solution. The general solution for a given potential V(x), is given by the linear combination: ψ(x,t) = ∑cnXnTn Our stationary states Xn remain the same!

why is the solution to the infinite square well not (A+B)e^(-xk^2)?

thx aloooot, you are great XD !!

thank you

What will happen if you have potential V(x) = 0, -a

but can't you only assume that B=0, if you have the potential well "starting" at x=0? i mean what's stopping you from putting the "borders", for lack of a better term, at per say, x=-2 and x=a where a is different to 0? or am i missing something crucial here?

Can you able to find electron between the two limits within the well?Even if the limited are not given??

1. I only have the answer for number 1. I think it's because the probability of finding the wave outside of the well is equal to zero so the psi function would be equal to zero as well. 2. I'm guessing because we can re-arrange the equation in such a way that we can use the real number solution for simple harmonic motion and it still preserves equality.

You're so good I can understand and I'm 12

at 13:45 how do you get Psi(x)=A Sin(npi/a x)? I don't understand how you reached the brackets of sin???

1. [h^2/(2m)ψ"(x)]/(V-E) = ψ(x) If general solution to the time-independent is still Asin(kx), it's clear the limit as v approaches infinity is 0. If the solution is not Asin(kx), then I don't know. 2. If ψ(x) = e^ikx, it will not be normalizable. I'm new to QM, and I'm still leaning. I don't think that I'm correct but I'd like to try.

how to calculate probability of for given energy

what happens when x=-L and x=L find average of position, square of position and momentum in ground state n=1

Answer according to me Q1 d2Ψ/dx2 will tend towards zero even if V tends to infinity as Ψ tends to 0. Q2 Ψ(x,t) = Asin(kx)exp(-iEt/h)

How does he write like that, some kind of touchscreen? I'd love to have something like that.

Ooooooooh man Thanks a lot your video helped me a lot

Hmm. Technically, the solution to the TISE is not Asin(kx)+Bcos(kx), but is Aexp(ikx)+Bexp(-ikx). Remember the wave function can be a complex function.

The only part I need help with is the simplification of sin((n*pi*x)/a)^2, A=srqt(2/a) really fell from the sky : what is the real mathematical proof ? I can't find it anywhere one the internet or in my lessons...

How probability wave function is equal to one?? What is the Physical meaning of it😐🤔

Good one

good

21:16 ...answers please?

I love you.

What is m?

Countering the arguments at the end: First: V(x) and d/dx2 are not simply scalars, but operators on the wavefunction ψ. In general, what operators do to a function can depend on the function they operate on. V(x) can be infinite in a region, but d/dx2 can still be 0 in the case that ψ = 0 in that region (which is exactly what our solution says). Second: Complex numbers can be real numbers. e^ikx is a real number if kx = nπ, which again is exactly what our solutions are! Thus we can simplify our expression by dropping the imaginary part of the expression, which is always 0. Thoughts?

man wanna learn literally whole quantum mechanics! it is interesting AF, but can't :( bcz of my syllabus

Thanks a lot for saving my ass

i understand that you're dealing with a time-independent case, but it seems very odd to me that an equation of a standing wave (a vibrating wave) can be described by an equation that does NOT depend on time. as a vibrating wave, it is surely EVOLVING over time, i.e. changing in shape. i think i've seen it's something to do with phase, i.e. that it's a wave of fixed shape which is effectively turning. but it is turning OVER time, surely! i'd be really grateful for any help please - please bear in mind i have no background in physics, but have done maths at uni

Please make a font of your handwriting xD

thank you