Moshinsky's shutter problem: an initial-value problem for the Klein–Gordon equation

Abstract

Moshinsky's problem is formulated and solved as a convolution integral. The initial data are discontinuous, giving the possibility of non-uniqueness. Asymptotic properties of the solution are deduced, using variants of the method of stationary phase. Comparisons are made with solutions of analogous problems for the one-dimensional wave equation and the Schrödinger equation.

Keywords:

• Klein–Gordon equation
• asymptotic analysis
• method of stationary phase
• non-uniqueness

AMS Subject Classifications:

• 35L15
• 35B40
• 41A60
• 81Q05

Notes

1. This formula is given incorrectly in the 1975 edition of 15.