THE PHASE FORMALISM FOR THE ONE-DIMENSIONAL EIGENVALUE PROBLEM AND ITS RELATION WITH THE QUANTUM BOHR-SOMMERFELD RULE

A quantum phase formalism is offered for searching for eigenvalues of the one-dimensional Schrodinger equation. Its application in the shooting method appreciably sped up convergence and made it absolute. The introduced quantum phase functions are close to their semiclassical analogues, unlike those used before, and transform into them in the semiclassical limit. A form of quantum analogue of the Bohr-Sommerfeld quantisation rule, allowing it to operate with non-integer quantum numbers within the framework of precise quantum consideration is obtained.