Title

The Phase Of A Quantum Mechanical Particle In Curved Spacetime

Document Type

Article

Publication Date

9-1-2001

Publication Title

General Relativity And Gravitation

Department

Science, Technology and Society

Abstract

We investigate the quantum mechanical wave equations for free particles of spin 0, 1/2, 1 in the background of an arbitrary static gravitational field in order to explicitly determine if the phase of the wavefunction is S/(h) over bar = integral p(mu) dx(mu)/(h) over bar, as is often quoted in the literature. We work in isotropic coordinates where the wave equations have a simple manageable form and do not make a weak gravitational field approximation. We interpret these wave equations in terms of a quantum mechanical particle moving in medium with a spatially varying effective index of refraction. Due to the first order spatial derivative structure of the Dirac equation in curved spacetime, only the spin 1/2 particle has exactly the quantum mechanical phase as indicated above. The second order spatial derivative structure of the spin 0 and spin I wave equations yield the above phase only to lowest order in (h) over bar. We develop a WKB approximation for the solution of the spin 0 and spin 1 wave equations and explore amplitude and phase corrections beyond the lowest order in (h) over bar, For the spin 1/2 particle we calculate the phase appropriate for neutrino flavor oscillations.

Volume

33

Issue

9

pp.

1459-1487

ISSN

0001-7701