The wave function of a particle subjected to a spherically symmetrical potential V (r) is given by

(a) Is Ψ an eigenfunction of L²? If so, what is the ! value? If not, what are the possible values of l that we may obtain when L² is measured?

(b) What are the probabilities for the particle to be found in vari ous m_l states?

(c) Suppose it is known somehow that Ψ(x) is an energy eigenfunction with eigenvalue E. Indicate how we may find V(r).

Transcribed Image Text:

(x) = (x+y+3z)f(r).