149 research outputs found
Quasi-plane waves for a particle with spin 1/2 on the background of Lobachevsky geometry: simulating of a special medium
In the paper complete systems of exact solutions for Dirac and Weyl equations
in the Lobachevsky space are constructed on the base of the method of
separation of the variables in quasi-cartesian coordinates. An extended
helicity operator is introduced. It is shown that solution constructed when
translating to the limit of vanishing curvature coincide with common plane wave
solutions on Minkowski space going in opposite z-directions. It is shown the
problem posed in Lobachevsky space simulates a situation in the flat space for
a quantum-mechanical particle of spin 1/2 in a 2-dimensional potential barrier
smoothly rising to infinity on the right.Comment: 33 page
Quasi-plane waves for spin 1 field in Lobachevsky space and a generalized helicity operator
Spin 1 particle is investigated in 3-dimensional curved space of constant
negative curvature. An extended helicity operator is defined and the variables
are separated in a tetrad-based 10-dimensional Duffin--Kemmer equation in quasi
Cartesian coordinates. The problem is solved exactly in hypergeometric
functions, the quantum states are determined by three quantum numbers. It is
shown that Lobachevsky geometry acts effectively as a medium with simple
reflecting properties. Transition to a massless case of electromagnetic field
is performed.Comment: 13 page
On solutions of the Pauli equation in non-static de Sitter metrics
A particle with spin 1/2 is investigated both in expanding and oscillating
cosmological de Sitter models. It is shown that these space-time geometries
admit existence of the non-relativistic limit in the covariant Dirac equation.
Procedure for transition to the Pauli approximation is conducted in the
equations in the variables , obtained after separating the angular
dependence of from the wave function. The non-relativistic
systems of equations in the variables is solved exactly in both
models. The constructed wave functions do not represent stationary states with
fixed energy, however the corresponding probability density does not depend on
the time.Comment: 12 page
Quantum Kepler problem for spin 1/2 particle in spaces on constant curvature. I. Pauli theory
Transition to a nonrelativistic Pauli equation in Riemann space of constant
positive curvature for a Dirac particle in presence of the Coulomb field is
performed in the system of radial equations, exact solutions are constructed in
terms of Hein functions, the energy spectrum is derived. The same is done for
the Kepler quantum problem in hyperbolic Lobachevsky space, solutions are
constructed in terms of Hein functions, the energy spectrum is obtained.Comment: 17 page
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