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

2011/04/20 by Tamás Gál, Tamas Gal, Gal, Tamas
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Spectroscopy and Quantum Chemical Studies #math-ph #math.MP #quant-ph

paper · pdf · doi:10.48550/arxiv.1104.4042

15 pages; determination of Morse index added

openalex publication_date 2011/04/20 · arxiv created 2011/04/26 · arxiv updated 2011/04/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

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.

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