Quantum Mechanics: Concepts and Applications · Problem 7.27

Identical Particles — Nouredine Zettili

Physics — Quantum Mechanics · spin-orbit-coupling-energy-levels

Problem

A particle of spin

\frac{1}{2}

is in a

d

state of orbital angular momentum (i.e.,

l = 2

). (a) What are its possible states of total angular momentum. (b) If its Hamiltonian is given by

H = a + b\hat{L}\cdot\hat{S} + c\hat{L}^2

, where

a

b

, and

c

are numbers, find the values of the energy for each of the different states of total angular momentum. Express your answer in terms of

a

b

c