A Path from the Quantization of the Action Variable to Quantum Mechanical Formalism

Anindya Biswas

Bertrand Berche, Ernesto A. Medina

V. Hushwater

Starting from the quantization of the action variable as a basic principle, and regarding the momentum and the energy of a particle as random functions of coordinates I arrive at the quantum mechanical formalism and the rule for probabilities in quantum mechanics. The discussion involves the correspondence principle and the assumption that the space-time symmetries known in classical physics are valid in the quantum domain.

Gin-yih Tsaur, Jyhpyng Wang

Eyad Hasan Hasan, Ola A. Jarab’ah, Khaled I. Nawafleh

This paper investigated the basic formalism for treating the dissipative Hamiltonian systems within the framework of the canonical method using the path integral quantization. The Hamiltonian treatment of the dissipative systems leads to obtain the equations of motion as a total differential equation in many variables which require the investigation of integrability conditions on the action and the equations of motion. In this formalism, the action integral for dissipative systems is obtained from equations of motion and written in phase space. Besides, the quantization of these systems is investigated using the action to construct the wave function in terms of the canonical phase space coordinates. Two examples are examined, the free particle and the simple harmonic oscillator.

Sol Wieder