Solving the Schrodinger Equation in 3D | Infinite Spherical Well (Spherical Bessel Functions)

In the previous video, we talked about the angular equation derived from the Schrodinger equation in three dimensions (3D). In this video, I talk about the radial part and as an example, I solve the radial part for the infinite spherical well for two cases: when l is zero and when l is not zero. We also talk about the effective potential and see how useful it is in solving the Schrodinger equation.
It's really important to say that in the case of the infinite well, there is a difference when solving the radial equation for angular quantum l zero. For non-zero angular quantum numbers, we reach the Bessel equation and we have to deal with Bessel functions. Bessel functions are like trigonometric functions, but they don't show a constant periodic behavior. So, what we can do is to just graph these functions and find the points where the Bessel function (for each l and m) intercepts with the x axis.
I hope this video help you to get a better sense about the radial equation and also how Bessel functions behave which are the wave functions for the infinite spherical well in three dimensions.











00:00 Radial Equation
01:16 Effective Potential
01:52 Infinite Spherical Well (l=0)
05:55 Infinite Spherical Well (non-zero l and Bessel Functions)


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In this series of videos I'm going to share some information about quantum physics based on the amazing book "Quantum Mechanics" by David J. Griffiths.

Quantum Physics playlist:
   • Quantum Physics