Relativistic quantum free particle in a non-stationary quasi-homogeneous field

Full Text : The one-dimensional motion of a relativistic quantum free particle in a nonstationary quasi homogeneous field has been considered. This exactly solvable problem has been formulated in the framework of a relativistic finite difference quantum mechanics. Wave function of the system in a relativistic configurationally X-representation has satisfied a mite difference equation, but in a momentum p-representation it has satisfied differential one. The equation of motion has been solved in a both momentum and configurationally representations by using an evolution operator of the system. We have also found a solution of a definite class of differential class of differential and finite difference equations. It was derived the new Baker-Hausdorff type operator identities