Quantization of the Wave Function

Antonio Díaz Miranda

Mikhail Karasev

Patrick Cornille

Matej Pavšič

A series of successive quantizations is considered, starting with the quantization of a non-relativistic or relativistic point particle: (1) quantization of a particle’s position, (2) quantization of wave function, (3) quantization of wave functional. The latter step implies that the wave packet profiles forming the states of quantum field theory are themselves quantized, which gives new physical states that are configurations of configurations. In the procedure of quantization, instead of the Schrödinger first-order equation in time derivative for complex wave function (or functional), the equivalent second-order equation for its real part was used. In such a way, at each level of quantization, the equation a quantum state satisfies is just like that of a harmonic oscillator, and wave function(al) is composed in terms of the pair of its canonically conjugated variables.

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.

Shan Gao