Work

Uniform operator: Aligning fractional time quantum mechanics with basic physical principles

Year: 2025

Type: article

Abstract: In this paper, we construct a fractional time corresponding operator to derive the uniform fractional time Schrödinger equation, which implies the relationship between the fractionaloperatorandtheenergy. Weverifythreebasicprinciplesoftheuniformfractional time Schrödinger equation: (a) Unitarity of the time evolution operator; (b) Existence of stationary energy spectra; (c) Probability conservation law. We apply the uniform equation to study three typical particles: free particle, an infinite potential well and a rectangular barrier. This uniform equation brings some typical physical phenomena, including (1) non-symmetry basic wave functions; (2) continuous energy spectrum for a free particle and an infinite potential well; (3) The barrier penetration in the rectangular barrier. These phenomena were not found in previous researches and the standard quantum mechanics, which will attract further applications in various fields of science.

Source: International Journal of Modern Physics A

DOI: 10.1142/s0217751x25500332

Authors: Xueling Duan, Cheng Ma, Hongyin Huang, Ke Deng

Institution: Sichuan University

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Natural Science Foundation of Sichuan Province

Award: G4484234408