Cases of structural equality between the scalar wave equations of optics and the quantum-mechanical Schrödinger equation

1992 ◽  
Vol 9 (6) ◽  
pp. 964 ◽  
Author(s):  
Hans Kragl
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Wave Equations ◽  
Quantum Mechanical ◽  
Scalar Wave

scholarly journals Generation of Time-Independent and Time-Dependent Harmonic Oscillator-Like Potentials Using Supersymmetric Quantum Mechanics

2018 ◽  
Vol 4 (1) ◽  
pp. 47-55
Author(s):  
Timothy Brian Huber
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Mechanical System ◽  
Schrodinger Equation ◽  
Supersymmetric Quantum Mechanics ◽  
Time Dependent ◽  
Quantum Mechanical ◽  
Quantum Mechanical System ◽  
Intertwining Operator

The harmonic oscillator is a quantum mechanical system that represents one of the most basic potentials. In order to understand the behavior of a particle within this system, the time-independent Schrödinger equation was solved; in other words, its eigenfunctions and eigenvalues were found. The first goal of this study was to construct a family of single parameter potentials and corresponding eigenfunctions with a spectrum similar to that of the harmonic oscillator. This task was achieved by means of supersymmetric quantum mechanics, which utilizes an intertwining operator that relates a known Hamiltonian with another whose potential is to be built. Secondly, a generalization of the technique was used to work with the time-dependent Schrödinger equation to construct new potentials and corresponding solutions.

scholarly journals Complex PT -symmetric nonlinear Schrödinger equation and Burgers equation

2013 ◽  
Vol 371 (1989) ◽  
pp. 20120059 ◽  
Author(s):  
Zhenya Yan
Keyword(s):  
Schrödinger Equation ◽  
Exact Solutions ◽  
Nonlinear Wave ◽  
Schrodinger Equation ◽  
Wave Equations ◽  
Burgers Equation ◽  
Kdv Equation ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Wave Equations ◽  
Nonlinear Schrödinger

The complex -symmetric nonlinear wave models have drawn much attention in recent years since the complex -symmetric extensions of the Korteweg–de Vries (KdV) equation were presented in 2007. In this review, we focus on the study of the complex -symmetric nonlinear Schrödinger equation and Burgers equation. First of all, we briefly introduce the basic property of complex symmetry. We then report on exact solutions of one- and two-dimensional nonlinear Schrödinger equations (known as the Gross–Pitaevskii equation in Bose–Einstein condensates) with several complex -symmetric potentials. Finally, some complex -symmetric extension principles are used to generate some complex -symmetric nonlinear wave equations starting from both -symmetric (e.g. the KdV equation) and non- -symmetric (e.g. the Burgers equation) nonlinear wave equations. In particular, we discuss exact solutions of some representative ones of the complex -symmetric Burgers equation in detail.

scholarly journals Quantum Mechanical Embedding of Spinning Particle and Induced Spin-Connection

1997 ◽  
Vol 12 (21) ◽  
pp. 1583-1588 ◽  
Author(s):  
Naohisa Ogawa
Keyword(s):  
Schrödinger Equation ◽  
Gauge Field ◽  
Schrodinger Equation ◽  
Quantum Mechanical ◽  
Spin Connection ◽  
Spinning Particle ◽  
Nonrelativistic Case

This letter introduces the method of the embedding of spinning particle quantum mechanically for nonrelativistic case. Schrödinger equation on its submanifold obtains the gauge field as spin-connection, and it reduces to the connection obtained by Ohnuki and Kitakado when we consider S2 in R3.

scholarly journals Membrane Topology Perturbation Theory of Wave Equations Developed from Schrodinger Equation in Gravitoetherton Superfluid Itself in Bohmian Pilot Waves

2021 ◽  
pp. 1-4
Author(s):  
Durgadas Datta ◽  
Keyword(s):  
Perturbation Theory ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Wave Equations ◽  
Membrane Topology ◽  
Relativity Theory ◽  
Modern Physics

Modern physics is suffering due to wrong interpretations of relativity theory and wrong Copenhagen interpretaions

Quantum Dynamics Using The Time-Dependent Schrödinger Equation

2006 ◽  
Author(s):  
Abraham Nitzan
Keyword(s):  
Schrödinger Equation ◽  
Quantum Dynamics ◽  
Schrodinger Equation ◽  
Time Dependent ◽  
Full Description ◽  
Quantum Mechanical ◽  
Condensed Phases ◽  
Full Picture ◽  
Linear Differential ◽  
External Forces

This chapter focuses on the time-dependent Schrödinger equation and its solutions for several prototype systems. It provides the basis for discussing and understanding quantum dynamics in condensed phases, however, a full picture can be obtained only by including also dynamical processes that destroy the quantum mechanical phase. Such a full description of quantum dynamics cannot be handled by the Schrödinger equation alone; a more general approach based on the quantum Liouville equation is needed. This important part of the theory of quantum dynamics is discussed in Chapter 10. Given a system characterized by a Hamiltonian Ĥ , the time-dependent Schrödinger equation is For a closed, isolated system Ĥ is time independent; time dependence in the Hamiltonian enters via effect of time-dependent external forces. Here we focus on the earlier case. Equation (1) is a first-order linear differential equation that can be solved as an initial value problem.

Sign in / Sign up

Export Citation Format

Share Document