Question

Find the possible values of energy of a particle of mass m located in a spherically symmetrical potential well U (r) = 0 for r < r₀ and U (r) = ∞ for r = r₀, in the case when the motion of the particle is described by a wave function ψ(r) depending only on r.

Instruction. When solving the Schrodinger equation, make the substitution ψ(r) = x (r)/r.

Answer 1

The Schrodinger equation is

(For r < r₀ we have rejected a term B cos k r as it does not vanish at r = 0). Continuity of the wavefunction at r = r₀  requires