Operator expansion in quantum mechanics

Abstract

Quasiclassical spectrum of Schroedinger equation is found by comparison of two expansions for Green's function—the operator expansion and the spectral one. A verification of the proposed method and its comparison with the method of the sum rules is performed for some kinds of potentials.

Keywords:

• Green's function
• Operator expansion
• Spectral expansion
• Sum rules
• Quasiclassical spectrum
• Euler–Maclaurin summation formula