Principles of Quantum Mechanics · Problem 12.6.5

The Hydrogen Atom — R. Shankar

Physics — Quantum Mechanics · radial-equation-nondegeneracy

Problem

Show that

D_l

is nondegenerate in the space of functions

U

that vanish as

r \to 0

. (Recall the proof of Theorem 15, Section 5.6.) Note that

U_{El}

is nondegenerate even for

E > 0

. This means that

E

l

, and

m

, label a state fully in three dimensions.