COX PARTICLE IN THE APPLIED MAGNETIC FIELD: ANALYSIS IN LOBACHEVSKY SPACE

The generalized Schrődinger equation for a scalar Cox particle is studied in the presence of a magnetic field on the background of Lobachevsky space. Separation of variables is performed. An equation describing the particle motion along the z axis appears to be much more complex than that when describing the Cox particle in Minkowski space. The form of the effective potential curve says that we have a quantum-mechanical problem of tunneling type. The derived equation has 6 regular singular points. Singular points 0 and 1 of the derived equation correspond to the physical domains z = ±∞. The solutions of the equation are constructed with the help of power series. Convergence of the series is examined by the Poincare – Perrone method. These series are convergent within the whole physical domain z ∈ (-∞,+∞). When considering an ordinary particle in Lobachevsky space, a simpler problem of tunneling type arises, which is exactly solved in terms of hypergeometric functions.

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