On a collinear collision between a particle and a harmonic oscillator with a Morse potential interaction

1974 ◽  
Vol 60 (7) ◽  
pp. 2934-2935 ◽  
Author(s):  
David A. Storm
Keyword(s):  
Harmonic Oscillator ◽  
Morse Potential ◽  
Potential Interaction

The Transfer Matrix Grid Method for Quantum Partition Functions, Eigenvalues and Eigenfunctions

1990 ◽  
Vol 45 (9-10) ◽  
pp. 1193-1198
Author(s):  
J. P. Prates Ramalho ◽  
F. M. Silva Fernandes
Keyword(s):  
Quantum Mechanics ◽  
Harmonic Oscillator ◽  
Transfer Matrix ◽  
Morse Potential ◽  
Grid Method ◽  
Hamiltonian Operator ◽  
Partition Functions ◽  
Feynman Path Integral ◽  
Feynman Path ◽  
Eigenvalues And Eigenfunctions

Abstract A method for the calculation of quantum partition functions, and bound eigenvalues and eigen-functions of the Hamiltonian operator is presented. The method is based on the discretization of the transfer matrix that relates the Feynman path integral to the conventional operator formulation of quantum mechanics. Its implementation is very simple, only requiring the diagonalization of the discretized transfer matrix. The method is applied to the harmonic oscillator and Morse potential. The results are in excellent agreement with the exact ones.

The Harmonic Oscillator

2018 ◽  
Author(s):  
Peter Mann
Keyword(s):  
Seventeenth Century ◽  
Probability Density Function ◽  
Harmonic Oscillator ◽  
Probability Density ◽  
Morse Potential ◽  
Superposition Principle ◽  
Quantum Field ◽  
Series Solutions ◽  
Robert Hooke ◽  
Dynamical Properties

This chapter discusses the harmonic oscillator, which is a model ubiquitous to all branches of physics. The harmonic oscillator is a system with well-known solutions and has been fully investigated since it was first developed by Robert Hooke in the seventeenth century. These factors ensure that the harmonic oscillator is as relevant to a swinging pendulum as it is to a quantum field. Due to the importance of this model, the chapter investigates its dynamical properties, including the superposition principle in solutions, and construct a probability density function in a single dimension. The chapter also discusses Hooke’s law, modes and the Morse potential. In addition, in an exercise, the chapter introduces series solutions to ordinary differential equations.

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