2 research outputs found
Moyal star product approach to the Bohr-Sommerfeld approximation
The Bohr-Sommerfeld approximation to the eigenvalues of a one-dimensional
quantum Hamiltonian is derived through order (i.e., including the
first correction term beyond the usual result) by means of the Moyal star
product. The Hamiltonian need only have a Weyl transform (or symbol) that is a
power series in , starting with , with a generic fixed point in
phase space. The Hamiltonian is not restricted to the kinetic-plus-potential
form. The method involves transforming the Hamiltonian to a normal form, in
which it becomes a function of the harmonic oscillator Hamiltonian.
Diagrammatic and other techniques with potential applications to other normal
form problems are presented for manipulating higher order terms in the Moyal
series.Comment: 27 pages, no figure