The Quantization of Integrable Systems

Abel Wolman

An integrable anharmonic oscillator is presumably simulable by a classical computer and therefore by a quantum computer. An integrable anharmonic oscillator whose Hamiltonian is of normal type and quartic in the canonical coordinates is not quantizable. If, as argued here, quantum simulation of a finitely realizable classical physical system entails quantization of that system, then either there exist nonsimulable, integrable anharmonic oscillators or there are no obstructions to quantization by simulation. Simulation quantization implies further that any obstructions to quantization arise entirely within the quantum domain.

Frank Willem Nijhoff, Hans W. Capel

Abel Wolman

An integrable anharmonic oscillator is presumably simulable by a classical computer and therefore by a quantum computer. An integrable anharmonic oscillator whose Hamiltonian is of normal type and quartic in the canonical coordinates is not quantizable. If, as argued here, quantum simulation of a finitely realizable classical physical system entails quantization of that system, then either there exist nonsimulable, integrable anharmonic oscillators or there are no obstructions to quantization by simulation. Simulation quantization implies further that any obstructions to quantization arise entirely within the quantum domain.

P. B. Guest

Miki Wadati, Taro Nagao, Kazuhiro Hikami

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.