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Schrodinger equation in Cylindrical Coordinates

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Please see the attach file, it cite from "Cohen Quantum Mechanics"

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The solution shows how to convert the operators to cylindrical coordinates and then how to utilize the common basis of eigenvectors in order to simplify Schrodinger equation in cylindrical coordinates.

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Three-Dimensional Time-Independent Schrodinger

A particle with mass m is confined inside of a spherical cavity of radius ro. The potential is spherically symmetric and can be written in the form: V(r)=0 for r<ro, and V(r)=infinity for r=ro. The particle is in the l=0 state.

(a) Solve the radial Schrodinger equation and use the appropriate boundary conditions to find the ground state radial wave function R(r) and the ground state energy.

(b) What is the pressure exerted by the particle (in the l=0 ground state) on the surface of the sphere?

Have will have something like this on the test soon and need to know how to do it. Outline of the solution please.

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