Abstract
In this paper nonconservative systems are investigated within the framework of Euler Lagrange equations. The solutions of these equations are used to find the principal function S, this function is used to formulate the wave function and then to quantize these systems using path integral method. One example is considered to demonstrate the application of our formalism.
Highlights
The path integral formulation of quantum mechanics is a description of quantum theory that generalizes the action principle of classical mechanics
Because the Euler Lagrange equations are second order equations, we find the equations of motion from the corresponding Lagrangian in terms of the generalized coordinates and their derivatives
This paper is mainly concerned with path integral quantization of nonconservative systems
Summary
The path integral formulation of quantum mechanics is a description of quantum theory that generalizes the action principle of classical mechanics. The basic idea of the path integral formulation can be traced back by [1] who introduced the Wiener integral for solving problems in diffusion and Brownian motion This idea was extended to the use of the Lagrangian in quantum mechanics [2]. The canonical formalism for investigating singular systems was developed by [4] [5] [6] In this formalism, the equations of motion are obtained as total differential equations. Depending on this method, the path integral quantization of constrained Lagrangian systems has been investigated by [7] [8] [9] [10].
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