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We present the exact solutions of one-dimensional Klein–Gordon and Dirac oscillators subject to the uniform electric field in the context of the new type of the extended uncertainty principle using the displacement operator method. The energy eigenvalues and eigenfunctions are determined for both cases. For the Klein–Gordon oscillator case, the wave functions are expressed in terms of the associated Laguerre polynomials and for the Dirac oscillator case, the wave functions are obtained in terms of the confluent Heun functions. The limiting cases are also studied using the special values of the physical parameters.

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The movement of a two-level atom interacting with an electromagnetic wave and subject to gravitation is studied using the path-integral formalism. The propagator is first of all written in the standard form D(path) exp(i/ )S(path) by replacing the spin by two fermionic oscillators; then it is determined exactly due to the auxiliary equation which has a cylindric parabolic function as a solution.

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