Lq. English et Rr. Winters, CONTINUED FRACTIONS AND THE HARMONIC-OSCILLATOR USING FEYNMANS PATH-INTEGRALS, American journal of physics, 65(5), 1997, pp. 390-393
The simple harmonic oscillator plays a prominent role in most undergra
duate quantum mechanics courses. The study of this system using path i
ntegrals can serve to introduce a formulation of quantum mechanics whi
ch is usually considered beyond the scope of most undergraduate course
s. However, given the current interest in the interpretation and found
ations of quantum mechanics, nonstandard approaches such as Feynman's
path integral formalism can be helpful in developing insights into the
structure of quantum mechanics. III this paper we evaluate the path i
ntegration appearing in Feynman's treatment in a natural and direct ma
nner utilizing a symbolic computational program. This approach makes t
he use of the path integral formulation of quantum mechanics accessibl
e to most undergraduate physics majors. As a by-produce of our approac
h, we find a representation of the reciprocal of the sine function, si
ne (x) = sin(x)/(x), in terms of an infinite product of partial approx
imates of a continued fraction. We have not found this representation
in the literature. (C) 1997 American Association of Physics Teachers.