On the semiclassical quantization condition

Jonathan M. Robbins

Paul Houle

E. Doron, Uzy Smilansky

Hiroshi Kuratsuji, Shinji Iida

Pablo A. Vicharelli, C. B. Collins

SongJJ, LiXG

The general quantization condition for periodic orbits in a two-dimensional integrable system is presented via the Berry-Tabor trace formula. Using the quantization and a periodicity condition of periodic orbits the semiclassical quantization condition and semiclassical quantized energies of a two dimensional uncoupled quartic oscillator system are given in detail. The semiclassical quantized energies-periodic orbits correspondence is also analysed.