Quantum Chemistry 3.7 - Particle in a Box Wavefunction Plots

Short lecture demonstrating particle in a box wavefunctions.

The particle in a box is a quantum mechanical model system for a particle which is restricted to a finite region of space. The potential energy is zero inside the box (zero to L) and infinite outside. The energy levels depend quadratically on a quantum number n [ E_n = h^2 n^2 / (8 m L^2) ] which is between 1 and infinity (n = 1, 2, 3, ...). The wavefunction is a half-integer number of sine waves inside the box [ psi_n(x) = sqrt(2 / L) sin(n pi x / L) ]. Quantum behavior disappears when you go to sufficiently large values of box length L and/or particle mass m.

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All TMP Chem content is free for everyone, everywhere, and created independently by Trent Parker.

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Microphone: Blue Yeti USB Microphone

Drawing Tablet: Wacom Intuos Pen and Touch Small

Drawing Program: Autodesk Sketchbook Express

Screen Capture: Corel Visual Studio Pro X8

[PunmasterSTP]

I was blown away at how amazing the visuals and explanation were, and though this video already has 35, 000 views (as of September 2022), it needs way, way more!

[gracedemalona]

What a great illustration of the effect of changing the different values! A really helpful tool, when trying to understand PIB! Thanks for this and all the other videos on quantum chemistry! Thanks to you, I learn and understand more and not the least - I passed my quantum chemistry-exam:-)

[markovdecisionprocess]

All the effort you put into your videos is greatly appreciated!

[ethan]

Awesome visual. I watched your other videos on this topic and you did a fantastic job at explaining things clearly and in detail. Thank you!

[simrannahar]

these are some amazingly well constructed videos, thank you so much!

[vijgenboom]

Great video! Many thanks. God bless you!

[raquellima]

This video is really great! Thank you very much!

[alimo]

Dear sir thanks a lot for your generous explanation, I really enjoy it.
I have a misunderstanding and appreciate if you could shed a light.
According to this video, the smaller box length (more confinement) is analogous to smaller wavelength. Am I right?
If I am right, then a particle in a box must have small wavelength to be treated as a quantum particle.
But, on the other hand, according to De Broglie, the wavelength for subatomic particles is much larger than that of classical objects.
Therefore, I am a bit confused here, why a De Broglie particle has a large wavelength while a particle in a box has small one?
Thanks a lot sir

[SampleroftheMultiverse]

I agree, very well done and informative! My process does not work when the probability density height is greater than one half of the wave length. Wondering how this translate into the quantum level. The graph of the energy to translate thru the energy levels I find interesting. I will send a copy of the test paper or view it on my channel. Anyone interested in seeing it.

[theodorehh]

Enjoyed your videos. Helped me understand Atkins better! Just out of curiosity, do you happen to specialise in computational/theoretical chemistry?

[giovana]

Hello! Your videos are awesome, very clean and simple!
Something that I didn't understand is the change in the value of the Planck's constant. In which cases we'll do this if always we consider h as the same value of 6.626×10^-34 m²kg/s?

[kitymaurya]

Sir pls make more videos on quantum chemistry...specially on perbutation theory