The spherically symmetric potential energy of a particle of mass μ is given by
V(r)={0∞a<r<belsewhere
where r=x2+y2+z2.
(a) Determine the ground-state energy.
(b) What is the ground-state position-space eigenfunction up to an overall normalization constant? What condition would you impose to determine this constant?
(c) What is the energy of the first excited l=0 state? Explain why it would not be so straightforward to determine the energy of the l=1 states.