Theoretical Physics

A Method to Evaluate Quantum Path Integrals

Download PDF (473.1 KB) PP. 7 - 13 Pub. Date: March 21, 2017

DOI: 10.22606/tp.2017.21002

Author(s)

Babak Vakili^*
Department of Basic Sciences, Tonekabon Branch, Islamic Azad University (IAU), Tonekabon, Iran

Abstract

As an alternative formulation of quantum mechanics, path integral is based on the notion of transition amplitude which gives the wave function of a quantum system at a time t_f by acting on the wave function at an earlier time t_i. We show that for a general quadratic form for the Lagrangian of the system, transition amplitude has the form f(t_f −t_i)e^i/hSclass. , where Sclass. is the classical action. We then present an algebraic method to evaluate the function f(t_f −t_i) without refereing to the path integral calculations. We examine the presented method to the cases of free particle and harmonic oscillator and obtain their propagators.

Keywords

Path integral, classical action.

References

[1] R.P. Feynman and A.R. Hibbs, Quantum Mechanics and Path Integrals, McGraw-Hill, New York, 1965.

[2] P.A.M. Dirac, The Principles of Quantum Mechanics, Oxford University Press, 1958. P.A.M. Dirac, Lectures on Quantum Mechanics, Dover Publications, New York, 1964.

[3] A. Das, Field theory, a path integral approach, Word Scientific Publishing, Singapore, 1993.

[4] R. Shankar, Principles of Quantum Mechanics, Plenum Press, New York, 1994.