The Hellmann–Feynman theorem, the comparison theorem, and the envelope theory

Abstract

The envelope theory is a convenient method to compute approximate solutions for bound state equations in quantum mechanics. It is shown that these approximate solutions obey a kind of Hellmann–Feynman theorem, and that the comparison theorem can be applied to these approximate solutions for two ordered Hamiltonians.

Keywords

• Envelope theory
• Hellmann–Feynman theorem
• Comparison theorem