If the three force constants in Prob. 4.20 are all equal, we have a three-dimensional isotropic harmonic oscillator.
(a) State why the wave functions for this case can be written as ψ = f(r)G(θ, ϕ).
(b) What is the function G?
(c) Write a differential equation satisfied by f(r).
(d) Use the results found in Prob. 4.20 to show that the ground-state wave function does have the form f(r)G(θ, ϕ) and verify that the ground-state f(r) satisfies the differential equation in (c).