95 v 2 8 M ar 2 00 3 Spin 0 and spin 1 / 2 quantum relativistic particles in a constant gravitaional field

The Klein-Gordon and Dirac equations in a semi-infinite lab (x > 0), in the background metric ds = u(x)(−dt + dx) + dy + dz, 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 mg~c. Finally, for nonzero transversemomentum, 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.