Geometric quantization rules in QCPB theory

TL;DR

This paper explores geometric quantization rules within the QCPB theory, extending quantum harmonic oscillator concepts with G-dynamics, and providing new operator formulations and quantization rules.

Contribution

It introduces geometric quantization rules based on QCPB theory and extends harmonic oscillator operators with G-dynamics, offering new mathematical frameworks.

Findings

Derived geometric creation and annihilation operators.

Formulated the geometric number operator.

Expressed the geometric Hamiltonian in a new form.

Abstract

Using the quantum covariant Poisson bracket (QCPB) theory, we can accomplish much more compatible explanations of the quantum mechanics supported by the G-dynamics. We further study the generalized quantum harmonic oscillator equipped with the G-dynamics of type I, such as geometric creation and annihilation operators, and the geometric number operator as an extension of the number operator is well given for the deep discussions, the geometric Hamiltonian operator is expressed as another form. Especially, the geometric quantization rules based on the QCPB theory is then calculated.