Question

A particle of mass m is located in a spherically symmetrical potential well U (r) = 0 for r < r₀ and U (r) = U₀ for r >r₀.

(a) By means of the substitution ψ(r) = x (r)/r find the equation defining the proper values of energy E of the particle for E < U₀, when its motion is described by a wave function ψ(r) depending only on r. Reduce that equation to the form

(b) Calculate the value of the quantity r²₀U₀ at which the first level appears.

Answer 1

These are exactly same as in the one dimensional problem