Particle in a Box Part 2: Interpreting the Results

In the previous tutorial we solved the Schrödinger equation for a quantum particle in an infinite square well. This is also known as the problem of the particle in a box. But there is a lot to unpack regarding the results, enough to merit its own tutorial in fact. So let's check out the orthogonality of the wavefunctions in the solution set, fine some expectation values, and go over some other subtle points.

Script by Hèctor Mas

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[noise_]

I started quantum mechanics on a masters with no real background. These videos gave me so much insight, a week ago i literally barely understood what a couple of symbols meant. Now i can see all the documentation and understand everything on them. For this i can’t thank professor dave enough. Now i need all the exercises to know how to tackle them!

[stringbean]

I hope maybe you'll see this at some point. I'm currently in my last semester of my chemistry degree and have a research presentation coming up that will determine whether I graduate or not.

My research involves synthesizing quantum dots and I was struggling to connect how the particle in a box model determines the wavelength the QDs absorb at. I could understand the model and I know that particle size determines the wavelength, but for the life of me I couldn't make them connect with the proper equations.

These two videos have finally put it all together for me and I couldn't be more grateful as I have a meeting with my professor in 10 hours. Now I won't look stupid for not being able to connect the fundamental concepts the entirety of my research is based on. An absolute blessing at 2:00 in the morning.

[guillermogini]

3:37 in the morning here...I have a quantum mechanics test today and I wish I'd found professor Dave's videos before. Thank you professor Dave! greetings from Moscow

[casperryde]

Very impressive how you can explain such difficult matter in such an easy way and using this ability to reach many people. Respect !👏👏👏

[vikasyadav]

Great Video. Awaiting other complex situations - Finite well, Harmonic oscillator, etc.

[RengodStablord]

This saved my butt today! Thank you so much for putting together such thorough content. I hope you are happy and healthy during these hard times.

[glennpearson]

Quantum mathematics made easy to understand. Also, recalling all those trigonometric identities was a fun trip down memory lane for me. Good stuff, Professor Dave! Oh, and it was nice to see a slightly different side of you on Catz's channel the other day. Take care and be safe.

[cgw]

Great video. Another way to see that <p>=0 is to use the symmetry x maps to a-x which preserves the system. This would send <p> to -<p>. But since it is the same system, we get <p> = -<p> so that <p>=0. Also, <T>=E since <V>=0 as V is either zero or the wavefunction is.

[bigbrothersinnerparty]

I think it would be better to upload hard concepts like these in a row as I have to rewatch most of these videos every time since I usually forget some of what I had learned before lol. Thanks for the great videos!

[che-maticschemistrymathema]

I'm so happy to have a teacher like you who knows everything 😍😍😍😍😍😍😍😍😍😍😍😍😍😍, Physics, Chemistry, Biology,

[criskity]

Imagine flat earthers trying to understand this. They'd just balk and say "Math isn't real!!"

[ManojKumar-cjoj]

Please, Dave ! Add some more videos in this brilliant series

[paulg]

His first part was great, but this is where he really delivers !

[eggieeeeeee]

Hi professor Dave, can you please upload videos in this series (modern physics), a little quicker, as I wait eagerly for these tutorials? Love you and all your tutorials.This is just my request. Stay happy. 🤗❤

[constancafigueiredo]

Thank you so much for your videos on Quantum Mechanics. It's so easy to understand when you explain it like that

[hidetsuguhiraki]

Your video series are always easy to understand. In physics, we must understand what equations mean in the real world. Your video series' detailed explanation is beneficial for my study of physics. Thank you very much, Sir.

[KrasaGalyaShararam]

Your videos on infinite potential box are superior! They helped me a lot. Thank you so much <3

[IslandHermit]

I'd always heard that quantum calculations were "difficult". After seeing this example I realize that most of the math itself is not difficult but rather the sheer amount of it required for even the simplest of problems.

[jesusdavidrinconpuche]

I've seen this problem since 2015 and I still think it's really interesting

[Релёкс]

16:30 perhaps an easier way to explain it is that the particle is constrained in a finite space so its average velocity (and thus momentum) has to be zero, and yet as we saw earlier it cannot have no energy so it has to be wobbling aroun, giving it a non zero average kinetic energy.