Abstract
The Klein–Gordon and Dirac equations are considered in a semiinfinite laboratory (x > 0) in the presence of background metrics ds2 = u2(x)ημν dxμ dxν and ds2 = -dt2 + u2(x)ηij dxi dxj with u(x) = e±gx. These metrics have nonconstant scalar-curvatures. Various aspects of the solutions are studied. For the first metric with u(x) = egx, it is shown that the spectra are discrete, with the ground state energy [Formula: see text] for spin-0 particles. For u(x) = e-gx, the spectrums are found to be continuous. For the second metric with u(x) = e-gx, each particle, depends on its transverse-momentum, can have continuous or discrete spectrum. For Klein–Gordon particles, this threshold transverse-momentum is [Formula: see text], while for Dirac particles it is g/2. There is no solution for u(x) = egx case. Some geometrical properties of these metrics are also discussed.
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