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(Solved): Particle in a 3D infinite potential well Suppose we have a particle in a 3D spherical and infinite ...
Particle in a 3D infinite potential well Suppose we have a particle in a 3D spherical and infinite potential well:
V(r)={(0,0<=r<=a),(\infty ,r>a):}where
(r,\theta ,\phi )are the radial and angular (spherical) coordinates. (a) Write down the time-dependent Schrödinger equation for the particle in spherical coor- dinates. (b) Use variable separation to split the spatial and temporal terms. What is the solu- tion for the temporal term? (c) Apply variable separation to the time-independent Schrödinger equation and write the differential equations of the radial and angular parts. Solve the angular equation. (d) Compute the energy levels and the stationary wave function,
\psi (r,\theta ,\phi )for
l=0.
