On the Choice of Method for Solution of the Vibrational Schrödinger Equation in Hybrid Statistical Physics - Quantum Mechanical Modeling of Molecular Solvation

2014 ◽  
pp. 187-196
Author(s):  
Bojana Koteska ◽  
Dragan Sahpaski ◽  
Anastas Mishev ◽  
Ljupčo Pejov
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Statistical Physics ◽  
Quantum Mechanical ◽  
Mechanical Modeling

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 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.

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.

ON A QUANTUM VERSION OF CONSERVATION LAWS FOR DERIVATIVE NONLINEAR SCHRÖDINGER EQUATION

1988 ◽  
Vol 03 (09) ◽  
pp. 893-900
Author(s):  
SHIBANI SEN ◽  
A. ROY CHOWDHURY
Keyword(s):  
Schrödinger Equation ◽  
Conservation Laws ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Quantum Mechanical ◽  
Conserved Quantities ◽  
Nonlinear Schrödinger ◽  
Quantum Version ◽  
Derivative Nonlinear Schrödinger Equation

We have derived the quantum mechanical versions of infinite number of conservation laws associated with Derivative Nonlinear Schrödinger equation with the help of a methodology used in string theory. The renormalised version of the conserved quantities are obtained with explicit forms of the counter terms.

scholarly journals Description of a free quantum-mechanical particle in the Lobachevsky space based on the integral equation

2019 ◽  
Vol 55 (3) ◽  
pp. 319-324
Author(s):  
Yu. A. Kurochkin
Keyword(s):  
Integral Equation ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Scattering Amplitude ◽  
Separation Of Variables ◽  
Free Particle ◽  
Classical Mechanics ◽  
Three Dimensional ◽  
Quantum Mechanical ◽  
Lobachevsky Space

The quantum mechanical problem of the motion of a free particle in the three-dimensional Lobachevsky space is interpreted as space scattering. The quantum case is considered on the basis of the integral equation derived from the Schrödinger equation. The work continues the problem considered in [1] studied within the framework of classical mechanics and on the basis of solving the Schrödinger equation in quasi-Cartesian coordinates. The proposed article also uses a quasi-Cartesian coordinate system; however after the separation of variables, the integral equation is derived for the motion along the axis of symmetry horosphere axis coinciding with the z axis. The relationship between the scattering amplitude and the analytical functions is established. The iteration method and finite differences for solution of the integral equation are proposed.

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