Proof of non-extremal nature of excited-state energies in nonrelativistic quantum mechanics with the use of constrained derivatives

Tamas Gal

Published 2011-04-20, updated 2011-04-26Version 2

With the use of a second derivative test based on constrained second derivatives, a proof is given that excited states in nonrelativistic quantum mechanics are saddle points of the energy expectation value, and is shown, further, how to determine their Morse index.