Improved Quantization Method of Coupled Circuits in Charge Discrete Space

Jin-Ying Ma, Weiran Zhao, Weilin Wang and Zhan-Yuan Yan ()
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Jin-Ying Ma: Department of Mathematics and Physics, North China Electric Power University, Yonghua North Street, Baoding 071003, China
Weiran Zhao: Department of Mathematics and Physics, North China Electric Power University, Yonghua North Street, Baoding 071003, China
Weilin Wang: Department of Mathematics and Physics, North China Electric Power University, Yonghua North Street, Baoding 071003, China
Zhan-Yuan Yan: Department of Mathematics and Physics, North China Electric Power University, Yonghua North Street, Baoding 071003, China

Mathematics, 2024, vol. 12, issue 23, 1-12

Abstract: A quantum theory of mesoscopic circuits, based on the discreteness of electric charges, was recently proposed. However, it is not applied widely, mainly because of the difficulty of the mathematical solution to the finite-difference Schrödinger equation. In this paper, we propose an improved perturbation method to calculate Schrödinger equations of the inductance and capacity coupling mesoscopic circuit. With a unitary transformation, the finite differential Schrödinger equation of the system is divided into two equations in generalized momentum representation. The concrete value of the parameter in circuits is important to solving the equation. Both the perturbation method suitable case and the improved perturbation method suitable case, the wave functions, and energy level of the system are achieved. As an application, the current fluctuations are calculated and discussed. The improved mathematical method would be helpful for the popularization of the quantum circuits theory.

Keywords: improved perturbation method; Mathieu function; quantum circuits theory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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