Dispositions as the Foundation for Feynman's Formulation of Quantum Mechanics

Philip L. Bowers

Tomasz Bigaj

Mario Di Mauro, Salvatore Esposito, Adele Naddeo

Maurice M. Mizrahi

L. Q. English, Ron Winters

The simple harmonic oscillator plays a prominent role in most undergraduate quantum mechanics courses. The study of this system using path integrals can serve to introduce a formulation of quantum mechanics which is usually considered beyond the scope of most undergraduate courses. However, given the current interest in the interpretation and foundations of quantum mechanics, nonstandard approaches such as Feynman’s path integral formalism can be helpful in developing insights into the structure of quantum mechanics. In this paper we evaluate the path integration appearing in Feynman’s treatment in a natural and direct manner utilizing a symbolic computational program. This approach makes the use of the path integral formulation of quantum mechanics accessible to most undergraduate physics majors. As a by-product of our approach, we find a representation of the reciprocal of the sinc function, sinc (x)≡sin(x)/(x), in terms of an infinite product of partial approximates of a continued fraction. We have not found this representation in the literature.

Mathieu Beau

In this article we present an analytic solution of the famous problem of diffraction and interference of electrons through one and two slits (for simplicity, only the one-dimensional case is considered). In addition to exact formulas, we exhibit various approximations of the electron distribution which facilitate the interpretation of the results. Our derivation is based on the Feynman path integral formula and this work could therefore also serve as an interesting pedagogical introduction to Feynman’s formulation of quantum mechanics for university students dealing with the foundations of quantum mechanics. 1 ha l-0