Quantum mechanics in formalism of dynamical time and Bohr-Sommerfeld quantization rule

A S Tarnovskiĭ

Petros N. Argyres

With the use of the Weyl correspondence between quantum mechanical operators and classical dynamical functions, an exact quantization rule is derived for a system with one degree of freedom and arbitrary Hamiltonian. In the semiclassical limit of small Planck's constant, this reduces to the Bohr-Sommerfeld quantization rule as derived by the WKB approximation. Higher order terms are also derived. It is further proven that for a simple harmonic oscillator the Bohr-Sommerfeld rule must give the exact energy eigenvalues for all states.

Sol Wieder

Y. B. Band, Y. Avishai

Robert G. Littlejohn

The Bohr-Sommerfeld and Maslov phases, which occur in the Einstein-Brillouin-Keller quantization rule of semiclassical mechanics, are shown to be examples of Berry's phase. The generalization of Berry's phase due to Aharonov and Anandan, which does not require adiabaticity, is employed.