Solutions of the d'Alembert and Klein-Gordon equations confined to a region with one fixed and one moving wall
Center for Theoretical Physics, Polish Academy of Sciences - Al. Lotników 32/46, 02-668 Warsaw, Poland, EU
Received: 23 January 2013
Accepted: 28 February 2013
General solutions of the Klein-Gordon equation satisfying the Dirichlet boundary conditions on one fixed wall and the other wall moving with a constant velocity are derived. These solutions are specified by an arbitrary periodic function whose period is equal to twice the value of the rapidity of the moving wall. Choosing this function as a combination of trigonometric functions one obtains the solutions derived recently by Koehn. The method is also tested in the case of the d'Alembert equation where it reproduces in a simple manner well-known results.
PACS: 03.65.Pm – Relativistic wave equations / 02.60.Lj – Ordinary and partial differential equations; boundary value problems / 03.65.Ge – Solutions of wave equations: bound states
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