Thermodynamics, Statistical Physics, and Quantum Mechanics

b) In order to determine the energy and potential, we operate on the eigen-

The constant in the last term can be simplified to

In the limit the potential vanishes, and only the constant term in

the kinetic energy equals the eigenvalue. Thus, we find

c) To find the potential we subtract the kinetic energy from the eigenvalue

The potential has an attractive Coulomb term and a repulsive

term.

5.23 Algebra of Angular Momentum (Stony Brook)

a)

b) Since and commute, we will try to find eigenstates with eigenvalues

state with the kinetic energy operator. For this gives for the radial

part

and act on the eigenfunction:

of and denoted by where are real numbers:

QUANTUM MECHANICS 267