Solving The Schrodinger Equation For An Electron In A Cylindrical Infinite Potential Well @DietterichLabs

Uploaded May 2018 | Updated September 2026, 2 days ago

The title is self explanatory.

My Quantum Mechanics Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsAFCzO-YWGlJ4TNv8sMdy

Superfluid Helium Resonance Experiment video:
youtu.be/unUNQNmuvUQ

Quantum Field Theory Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsk7BSZjONcfhRGKNa2uou

At 7:02, there are a couple of obvious typos where I have n^2 where I should have n^2Pi^2/l^2. Also, there is a sign error in the same area. These errors are easily corrected, and are not propagated throughout the rest of the calculation.

Another typo was found. The normalization factor for the angular part is supposed to be (2Pi)^(-1/2) instead of (2Pi)^(1/2). I missed the negative sign in the exponent.

Typo: the normalization constant for the theta part should be 1 over what is shown.

Solving The Schrodinger Equation For An Electron In A Cylindrical Infinite Potential Well

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$Did I Get This Right? Tell Me In The Comments (see description for corrections/additional details) Attempting To Break Down The Quantum Many Body Problem | Schrodinger Equation | Dirac Equation In this video, I try to break apart the multi-electron atom many body problem in quantum mechanics. I attempt to do this using kind of a weird ansatz that I constructed specifically for this application. Let me know what you think of my attempt in the comments! There is a typo in the spherical harmonics normalization constant. In the second fraction under the square root, the 1s are supposed to be ls. Also, its worth noting that if the general solution is right, you could generalize to an arbitrary quantum Coulombic many-body problem, by just including coulomb potential terms with the appropriate sign and charge magnitude, and then propagating that accordingly throughout the solution. One could also include no stationary charges. This is just a change of parameterization. Pairings involving differing masses requires an obvious adjustment of the coordinates to resolve the kinetic terms in the same way. 3/19/2023: I realized recently that I know longer remembered how I justified the formulas I gave in this video for the hatted quantum numbers. In the video, I gave no detailed explanation. I simply said something about normalizability. I therefore decided to sit down and work it out again. I found that the formulas I gave in the video are wrong, and the fully detailed justification (which I meticulously recorded this time) for the justification for replacement formulas leverages much more than normalizability. The following link takes you to a page where I have a new educated guess for the correct formulas, and their justification: https://twitter.com/DietterichLabs/status/1638026174969389056 3/20/2023: It is worth noting that I only chose the hydrogen-like solutions for phi as a starting point. I figured that I might find solutions with the right properties within (a generalized set) of them. Had this not worked, I would have looked at other solutions. I did not assume that a solution form from a bound state problem would necessarily be the correct idea for a repulsive potential. 8/7/2023: In the general multi-electron atom solutions that I gave to the Schrodinger and Dirac equations, I included a number of summation and product symbols, which are supposed to generate all of the correct factors and terms. Im not entirely sure that they do so perfectly, but the intended design should be clear. In the Schrodinger case, there are the usual H-atom factors for each nucleus-electron interaction, as well as a difference-coordinate H-atom factor and a corresponding greens function term for each electron-electron interaction. In the Dirac equation, the greens function terms are unnecessary. 1/26/2024: It turns out that these new eigenvalues are also wrong. Here is a link to an updated video: https://youtu.be/-xLhrYA6TNU Here is the link to my video on solving the Dirac equation for the hydrogen atom: https://www.youtube.com/watch?v=jWYtP-rAoYA Here is my video on solving the Schrodinger equation for the hydrogen atom: https://www.youtube.com/watch?v=MaXFT-c8u1E In both of these videos, I actually address the general one-electron atom. I dont bother setting Z=1. This, of course, includes the hydrogen atom. For those who are curious, I also have a video on how to solve the Klein-Gordon equation for the one-electron atom: https://www.youtube.com/watch?v=9_3uQdF-tEs Superfluid Helium Resonance Experiment video: https://youtu.be/unUNQNmuvUQ Quantum Field Theory Lecture Series: https://www.youtube.com/playlist?list=PLSpklniGdSfSsk7BSZjONcfhRGKNa2uou$ $Spherical Quantum Harmonic Oscillator | Schrodinger Equation | Quantum Mechanics In this video, I show you how to solve the Schrodinger equation for the 3D spherical quantum harmonic oscillator. One Clarification And 1 Typo: The Clarification: It is apparent from the math, but the quantum number n here must be a positive even integer. The Typo: The typo is in the normalization constant of the radial wavefunction. There is supposed to be a double factorial after the parentheses in the denominator. My Quantum Mechanics Lecture Series: https://www.youtube.com/playlist?list=PLSpklniGdSfSsAFCzO-YWGlJ4TNv8sMdy There is a typo in the spherical harmonics normalization constant. In the second fraction under the square root, the 1s are supposed to be ls. Superfluid Helium Resonance Experiment video: https://youtu.be/unUNQNmuvUQ Quantum Field Theory Lecture Series: https://www.youtube.com/playlist?list=PLSpklniGdSfSsk7BSZjONcfhRGKNa2uou$

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Solving The Schrodinger Equation For An Electron In A Cylindrical Infinite Potential Well