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Spin 0 and spin 1/2 quantum relativistic particles in a constant gravitational field

M. Khorrami·M. Alimohammadi·A. Shariati
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Abstract

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 + g x$. 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 $mg\hbar c$. Finally, for nonzero 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.

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M. Khorrami, M. Alimohammadi, A. Shariati. 2003-03-08. Spin 0 and spin 1/2 quantum relativistic particles in a constant gravitational field. https://doi.org/10.1016/s0003-4916(03)00016-2

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