Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

理论物理通讯：英文版

Determining Energy Eigenvalues of Dynamic Systems by Finding ＇Eigen-operator＇ ofSquare of Schroedinger Operator

FANHong-Yi, XUXue-Fen, Lichao

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

A newly transparent approach for determining energy eigenvalues is proposed, which is finding the ‘eigen-operator' of the square of the Schroedinger operator. As three examples, we discuss the energy level of a nondegenerate parametric amplifier, an angular momentum system and a ring shape of coupled oscillators.

Related papers

Determining Energy Eigenvalues of Dynamic Systems by Finding ‘Eigen-operator’ of Square of Schrödinger Operator

Fan Hong‐Yi, Xuefen Xu, Li Chao

A newly transparent approach for determining energy eigenvalues is proposed, which is finding the 'eigenoperator' of the square of the Schrodinger operator. As three examples, we discuss the energy level of a nondegenerate parametric amplifier, an angular momentum system and a ring shape of coupled oscillators.

Communications in Theoretical Physics•Dec 15, 2004•5 citations

“Eigen-Operator” Method of the Square of Schroedinger Operator in Interaction Picture and Its Application in Describing Parametric Amplifiers

Fan, Hong-Yi, Yue Yue

我们扩大寻找 theSchrodinger 操作员的平方的“ eigen 操作员”到相互作用图画的方法，它不仅帮助构造二种参量的放大器的 Hamiltonians 而且导致考虑到免费 Hamiltonian 和交往的 Hamiltonian 的一种新不确定性关系。

理论物理通讯：英文版•Jan 1, 2005•0 citations

``Eigen-Operator" Method of the Square of Schrödinger Operator in Interaction Picture and Its Application in Describing Parametric Amplifiers

Hong-Yi Fan, Yue Fan

We extend the method of searching ``eigen-operator" of the square of the Schrödinger operator to the interaction picture, which not only helps to construct Hamiltonians of two kinds of parametric amplifiers but also leads to a new uncertainty relation regarding to the free Hamiltonian and the interacting Hamiltonian.

Communications in Theoretical Physics•Aug 1, 2005•3 citations

DETERMINATION OF THE EIGEN-ENERGIES AND FUNCTIONS FROM THE MAXWELL- BOLTZMANN DENSITY OPERATOR. II. CASE OF PERTURBED SYSTEMS

Pieter Smet, Jacques Tillieu

Previously described methods for the determination of eigen-energies and corresponding projectors from the Maxwell-Boltzmann density operator are adapted to a perturbed system. As an example, the anharmonic oscillator problem is examined. (auth)

•Nov 1, 1962•0 citations

The Schrödinger Equation in Three Dimensions

Donald Gary Swanson

In the previous chapter, the postulates helped us to use the wave function to find the expected results of experimental measurements by letting a dynamical quantity F (x, p, t) → F (xˆ, pˆ, t) and integrating over space. In the examples, however, the wave functions were typically given and not derived from first principles. We now endeavor to find the appropriate wave functions for a variety of physical systems in one dimension by solving the Schro¨dinger equation where for time-independent cases, the total energy is an eigenvalue. In subsequent chapters, we will extend the method to three dimensions and develop the appropriate operators, eigenvalues, and eigenfunctions for angular momentum. We will also develop methods for examining time-dependent systems. The latter chapters address special systems of interest that may be referred to as applications of quantum mechanics.

Taylor & Francis eBooks•Aug 9, 2006•0 citations

Energy-Level of Some Singular Harmonic Oscillators and Parametric Amplifiers with Singular Potential Derived via IEO Method

Fan, Hong-Yi, Tang +1 more

我们采用不变的 eigen 操作员(IEO ) 发现 N 身体单个振荡器的 Hamiltonians 的 invarianteigen 操作员然后导出他们的精力的方法豁开。有单个潜力的参量的放大器的 TheHamiltonians 也这样被讨论。

理论物理通讯：英文版•Jan 1, 2007•1 citation
In the previous chapter, the postulates helped us to use the wave function to find the expected results of experimental measurements by letting a dynamical quantity F (x, p, t) → F (xˆ, pˆ, t) and integrating over space. In the examples, however, the wave functions were typically given and not derived from first principles. We now endeavor to find the appropriate wave functions for a variety of physical systems in one dimension by solving the Schro¨dinger equation where for time-independent cases, the total energy is an eigenvalue. In subsequent chapters, we will extend the method to three dimensions and develop the appropriate operators, eigenvalues, and eigenfunctions for angular momentum. We will also develop methods for examining time-dependent systems. The latter chapters address special systems of interest that may be referred to as applications of quantum mechanics.