Jilin Normal University Journal

Solving Hamiltonian of Coupling Oscillators and RLC Quantization Circuit by Unitary Operator

Qiangchun Liu

Published Jan 1, 2010• 0 citations

Abstract

For coupled oscillators and RLC quantization circuit whose Hamiltonian have been given by H =p 22m+γ(q p +p q )+12mω2q 2 and H =p 22L+R2L(q p +p q )+12Cq 2,respectively,a method of eliminating the coupled item for unitary operators are presented.The energy eigen values of coupling oscillators and RLC quantization circuit obtained by this bandy method are in good agreement with the date calculated by Schrdinger equation.This method could train and improve the ability of students in solving complicated physics problems with quantum mechanics.

Related papers

Quantization in mesoscopic RLC coupled circuit of two meshes

Han Yue-Wu

Starting from the equation of the mesoscopic coupled circuits,we study the quantization in mesoscopic RLC coupled circuit of two meshes by using the canonical transformation.The results reveal that its Hamiltonian is unitary equivalent to that of two independent harmonic oscillators.

College PhysicsJan 1, 20090 citations

Deriving the energy-level gap of coupled two atoms molecule by invariant eigen-operator method

Yijun Yang

The energy-level gaps for coordinate coupled and momentum coupled two atoms molecule are presented by using invariant eigen-operator method within Heisenberg equation.The results obtained by this bandy method are in good agreement with the date calculated by Schrdinger equation.This method could train and improve the ability of students in solving complicated physics problems with quantum mechanics.

Jan 1, 20100 citations

Quantum fluctuations of charge and current in RLC circuit

Wang Zhong-chen, Guo Zheng-ping

Starting from equation of motion of the active RLC circuit,we adopt the technique of the unitary transformation,transform the charge and current into the unitary variable and then have the quantization.By making use of standard transformation,we try to solve the time equation.For the application,quantum fluctuations of charge and the current in the mesoscopic circuit in the harmonic oscillator state are studied,result is analyzed and discussed.

Journal of Qingdao Technological UniversityJan 1, 20060 citations

On Selection of Unitary Operator in Quantizing Process of Mesoscopic RLC Circuit with a Power Source

Zhu Ai-dong

The mesoscopic RLC circuit with a power source is quantized using the methods of canonical transformation and unitary transformation. By analyzing and comparing the calculation processes of several different unitary operators, we obtain the most appropriate scheme to build an unitary operator which enables the results of canonical transformation and unitary transformation to be same with each other.

Acta Sinica Quantum OpticaJan 1, 20030 citations

Improved Quantization Method of Coupled Circuits in Charge Discrete Space

Jinying Ma, Weiran Zhao, Weilin Wang +1 more

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.

MathematicsNov 28, 20241 citation

Time-dependent coupled harmonic oscillators: Classical and quantum solutions

D. X. Macedo, I. Guedes

In this work we present the classical and quantum solutions for an arbitrary system of time-dependent coupled harmonic oscillators, where the masses (m), frequencies (ω) and coupling parameter (k) are functions of time. To obtain the classical solutions, we use a coordinate and momentum transformations along with a canonical transformation to write the original Hamiltonian as the sum of two Hamiltonians of uncoupled harmonic oscillators with modified time-dependent frequencies and unitary masses. To obtain the exact quantum solutions we use a unitary transformation and the Lewis and Riesenfeld (LR) invariant method. The exact wave functions are obtained by solving the respective Milne–Pinney (MP) equation for each system. We obtain the solutions for the system with m1 = m2 = m0eγt, ω1 = ω01e-γt/2, ω2 = ω02e-γt/2 and k = k0.

International Journal of Modern Physics EAug 25, 20144 citations