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The Green’s function relative to the one-dimensional Natanzon potentials is exactly calculated by the path integral approach. The energy spectrum, the wave functions, and the scattering function S are deduced.

We present the solution of Duffin-Kemmer-Petiau (DKP) equation of spin 0 and 1 in the case of the time-dependent mass in the presence of a time-dependent linear scalar field. Calculation is carried out analytically, the wave functions are then deduced for both cases and are connected respectively to the auxiliary equations. The adiabatic approximation is deduced and reveals that in this study we have an obvious absence of the geometrical amplitude factor.

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