General Methods of Quantum Mechanics

MASSIMO RUDAN

Leon W. Cohen

While it is generally accepted that quantum mechanics is a probability theory, its methods differ radically from standard probability theory. We use the methods of quantum mechanics to understand some fundamental aspects of standard probability theory. We show that wave functions and operators do appear in standard probability theory. We do so by generalizing the Khintchine and Bochner criteria for a complex function to be a characteristic function. We show that quantum mechanics clarifies these criteria and suggests generalizations of them.

James E. House

K. S. Cheng

The equivalent Lagrangians for a generalized mechanical system are defined and the effects of using different members of the class of equivalent Lagrangians in classical mechanics and quantum mechanics are discussed. The path integration method is applied to quantize the generalized mechanical system.

Wolfgang Ernst Friederich Pauli

Won Sang Chung

In this paper, we discuss the quantum mechanics with the generalized uncertainty principle (GUP) where the commutation relation is given by [Formula: see text]. For this algebra, we obtain the eigenfunction of the momentum operator. We also study the GUP corrected quantum particle in a box. Finally, we apply the factorization method to the harmonic oscillator in the presence of a minimal observable length and obtain the energy eigenvalues by applying the perturbation method.