68 research outputs found
On Dirac theory in the space with deformed Heisenberg algebra. Exact solutions
The Dirac equation has been studied in which the Dirac matrices
\hat{\boldmath\alpha}, \hat\beta have space factors, respectively and
, dependent on the particle's space coordinates. The function deforms
Heisenberg algebra for the coordinates and momenta operators, the function
being treated as a dependence of the particle mass on its position. The
properties of these functions in the transition to the Schr\"odinger equation
are discussed. The exact solution of the Dirac equation for the particle motion
in the Coulomnb field with a linear dependence of the function on the
distance to the force centre and the inverse dependence on for the
function has been found.Comment: 13 page
Behavior of the impurity atom in a weakly-interacting Bose gas
We studied the properties of a single impurity atom immersed in a dilute Bose
condensate at low temperatures. In particular, we perturbatively obtained the
momentum dependence of the impurity spectrum and damping. By means of the
Brillouin-Wigner perturbation theory we also calculated the self-energy both
for attractive and repulsive polaron in the long-wavelength limit. The
stability problem of the impurity atom in a weakly-interacting Bose gas is also
examined.Comment: 11 pages, 4 figure
Kepler problem in Dirac theory for a particle with position-dependent mass
Exact solution of Dirac equation for a particle whose potential energy and
mass are inversely proportional to the distance from the force centre has been
found. The bound states exist provided the length scale which appears in
the expression for the mass is smaller than the classical electron radius
. Furthermore, bound states also exist for negative values of
even in the absence of the Coulomb interaction. Quasirelativistic expansion of
the energy has been carried out, and a modified expression for the fine
structure of energy levels has been obtained. The problem of kinetic energy
operator in the Schr\"odinger equation is discussed for the case of
position-dependent mass. In particular, we have found that for highly excited
states the mutual ordering of the inverse mass and momentum operator in the
non-relativistic theory is not important.Comment: 9 page
Theory Of Radiation And Absorption Of Deformed Field Quanta
We calculate the intensity of spontaneous radiation of a system of non-linear
quantum field, where the non-linearity is due to deformations of the Poison
brackets of the generalized coordinates and momenta.Comment: This paper is dedicated to Professor Igor Stasyuk on the occasion of
his 70th birthday. 9 pages, 1 figur
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