Quantum Chemistry 3.5 - Particle in a Box

Short lecture on particle in a box wavefunctions and energies.

The particle in a box is a model system for a particle which is constrained to a finite region of space. The potential energy is zero inside the box (zero to L) and infinite outside the box. We substitute this potential energy function into the Schrodinger equation and solve for the wavefunction and the energy levels of the particle in a box. Using the boundary conditions that the wavefunction must be zero at the edges of the box, we determine that the wavefunctions are a half integer of a sine wave inside the box. The energy depends quadratically on the positive quantum number n (n = 1, 2, 3), inverse with mass, and inverse quadratic with the length of the box.

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[salimdebit]

Thank you so much for the great explanation ! I live in Algeria and I'm a first year college student in industrial sciences. At the chemistry course they just tell us to skip the pure mathemetical part of quantum chemistry and simply apply it to quantum numbers and orbitals. I always wanted to truly get the math behind it, and your channel is exactly what I needed. Thank you again sir !

[rebekkakanerva]

My material science prof decided not to go over this at all because "surely you've all already familiar with the Schrödinger equation", which we chemistry students, in fact, were not. So this was such a great and clear explanation of this model! Thank you!

[rodrigogomes]

Your explanation was fabulous. I've been struggling a bit with quantum chem at my uni and it made everything clear about the particle in a box. Thank you! Salutations from Brazil.

[vincentm]

Absolutely brilliant, and you're answering every important question in the comments, what a good teacher. Thanks for all your work!

[naturematters]

I got stuck on a video about the maxwell boltzmann distribution in a channel called tonya coffey (great channel by the way) because of this very concept of energy in different nodes of waves so i searched online in google and youtube i found this video which i will definitely share this with my quantum enthusiastic friends. Amazing video TMP
from India

[photon]

its actually awesome that you reply to people in the comment section!

[PunmasterSTP]

PIB? More like "Perfect videos for me!" Thanks for sharing.

On another note, the first time I saw this material I thought it was so cool that we could derive a "quantum number", after having seen them being described (but not derived) in gen chem.

[vaishalishayoni]

Your video are really helping me a lot in understanding quantum chemistry...

[pitampaul]

Your explanation was much specific and clear than many of the Indian youtubers. Really grateful to find you on youtube.

[azwasaleem]

This topic is crystal clear to me now... Thank you so much..

[ae]

Thank you so much for these. Revising for collections and these are so helpful!!!

[Amr-nedl]

Thank you for your effort! These videos have been of great help.

[jacobvandijk]

@ 2:35 Remember that 2.m.E = 2.m.(1/2.m.v^2) = m^2 . v^2 = p^2 . So k = p / h-bar !
@ 6:54 There is only 1 quantum-number here because this is a 1-dimensional situation.

[amenemhurt]

Outstanding elaboration. I wish You Tube was available back in 1988 when I first took QC course 🙄🙄

[iqrahamid]

When you took x= l part why did you exclude the cosine part

[arcanuke]

Is there any more elegant way of finding the form of psi than by just guessing that it should be of the form Asinkx+Bcoskx and differentiating twice to find what k should be? I was looking for some way of finding that sin and cos form rather than just knowing it.

[tag_of_frank]

In contrast to the normal wave equation whose solution is a linear combination of the eigenfunctions, here, because of quantization of energy, must the solution be only ONE of the eigenfunctions?

[amishasaxena]

really nice and easy to understand videos.... all the conceptual doubts get cleared...

[ektashuklaaa]

Thankyou sir. I want to know if the boundaries of the well are -L/2 to L/2, what will be the energy ?

[sachbrad]

why have you taken an extra wave function in the Hamiltonian operator when simplifying H* wave function= E*wavefunction ?