The Klein-Gordon and Dirac equations in a semi-infinite lab (x > 0), in the background metric ds(2) = u(2) (x) (- dt(2) + dx(2)) + dy(2) + dz(2), are investigated. The resulting equations are studied for the special case u(x) = 1 + gx. It is shown that in the case of zero transverse-momentum, the square of the energy eigenvalues of the spin-1/2 particles are less than the squares of the corresponding eigenvalues of spin-0 particles with same masses, by an amount of mghc. Finally, for non-zero transverse-momentum, the energy eigenvalues corresponding to large quantum numbers are obtained and the results for spin-0 and spin-1/2 particles are compared to each other. (C) 2003 Elsevier Science (USA). All rights reserved. [References: 13]
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