From quantization in phase space to functions of quantum numbers

Shuang-Bo Yang

For two kinetically coupled identical Morse oscillator system, this paper introduced the concept of quantum torus wave function. Quantum torus wave function comes from the decomposition of a quantum wave function of the system. It reflects the symmetry of the quantum wave function. Physically, it corresponds to a quantizing torus or a quantizing cantorus (when it exists) in phase space. The number of nodes in x and y coordinates in the contour plot, being the same as the quantum number in the Einstein-Brillouin-Keller (EBK) quantization conditions, is the natural assignment of the given energy level. When quantizing torus or cantorus is destroyed by weak resonances in phase space, using quantum torus wave function to assign energy level is easier and reasonable. This paper also shows the application of quantum torus wave function in the study of dynamical tunneling.

Carlos Alberto Alcalde, Kanishka Tyagi

Christopher J. Fewster, Hanno Sahlmann, Strings and Elementary Particles Quantum Gravity +1 more

We give a definition for the Wigner function for quantum mechanics on the Bohr compactification of the real line and prove a number of simple consequences of this definition. We then discuss how this formalism can be applied to loop quantum cosmology. As an example, we use the Wigner function to give a new quantization of an important building block of the Hamiltonian constraint. 1

James A. Brooke, Franklin E. Schroeck

Kazuma Nagao

Christopher J. Fewster, Hanno Sahlmann

We give a definition for the Wigner function for quantum mechanics on the Bohr compactification of the real line and prove a number of simple consequences of this definition. We then discuss how this formalism can be applied to loop quantum cosmology. As an example, we use the Wigner function to give a new quantization of an important building block of the Hamiltonian constraint.