Quantum normal forms, Moyal star product and Bohr–Sommerfeld approximation
Quantum normal forms, Moyal star product and Bohr–Sommerfeld approximation
The Bohr-Sommerfeld approximation to the eigenvalues of a one-dimensional quantum Hamiltonian is derived through order $\hbar^2$ (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 $\hbar$, …