29 research outputs found
Coherent States and a Path Integral for the Relativistic Linear Singular Oscillator
The SU(1,1) coherent states for a relativistic model of the linear singular
oscillator are considered. The corresponding partition function is evaluated.
The path integral for the transition amplitude between SU(1,1) coherent states
is given. Classical equations of the motion in the generalized curved phase
space are obtained. It is shown that the use of quasiclassical Bohr-Sommerfeld
quantization rule yields the exact expression for the energy spectrum.Comment: 14 pages, 2 figures, Uses RevTeX4 styl
Exact solution of the position-dependent mass Schr\"odinger equation with the completely positive oscillator-shaped quantum well potential
Two exactly-solvable confined models of the completely positive
oscillator-shaped quantum well are proposed. Exact solutions of the
position-dependent mass Schr\"odinger equation corresponding to the proposed
quantum well potentials are presented. It is shown that the discrete energy
spectrum expressions of both models depend on certain positive confinement
parameters. The spectrum exhibits positive equidistant behavior for the model
confined only with one infinitely high wall and non-equidistant behavior for
the model confined with the infinitely high wall from both sides. Wavefunctions
of the stationary states of the models under construction are expressed through
the Laguerre and Jacobi polynomials. In general, the Jacobi polynomials
appearing in wavefunctions depend on parameters and , but the Laguerre
polynomials depend only on the parameter . Some limits and special cases of
the constructed models are discussed.Comment: 20 pages, 4 figure
The Wigner function of a q-deformed harmonic oscillator model
The phase space representation for a q-deformed model of the quantum harmonic
oscillator is constructed. We have found explicit expressions for both the
Wigner and Husimi distribution functions for the stationary states of the
-oscillator model under consideration. The Wigner function is expressed as a
basic hypergeometric series, related to the Al-Salam-Chihara polynomials. It is
shown that, in the limit case (), both the Wigner and Husimi
distribution functions reduce correctly to their well-known non-relativistic
analogues. Surprisingly, examination of both distribution functions in the
q-deformed model shows that, when , their behaviour in the phase space
is similar to the ground state of the ordinary quantum oscillator, but with a
displacement towards negative values of the momentum. We have also computed the
mean values of the position and momentum using the Wigner function. Unlike the
ordinary case, the mean value of the momentum is not zero and it depends on
and . The ground-state like behaviour of the distribution functions for
excited states in the q-deformed model opens quite new perspectives for further
experimental measurements of quantum systems in the phase space.Comment: 16 pages, 24 EPS figures, uses IOP style LaTeX, some misprints are
correctd and journal-reference is adde
The Husimi function of a semiconfined harmonic oscillator model with a position-dependent effective mass
The phase space representation for a semiconfined harmonic oscillator model
with a position-dependent effective mass is constructed. We have found the
Husimi distribution function for the stationary states of the oscillator model
under consideration for both cases without and with the applied external
homogeneous field. The obtained function is expressed through the double sum of
the parabolic cylinder function. Different special cases and the limit
relations are discussed, too.Comment: 12 pages, 8 figure
The Wigner function of a semiconfined harmonic oscillator model with a position-dependent effective mass
We develop a phase-space representation concept in terms of the Wigner
function for a quantum harmonic oscillator model that exhibits the
semiconfinement effect through its mass varying with the position. The new
method is applied for the analytical computation of the Wigner distribution
function for such a semiconfinement quantum system. The method allows for
suppression of the divergence of the integrand in the definition of the quantum
distribution function and leads to the computation of its analytical
expressions for the stationary states of the semiconfined oscillator model.
Both cases of the presence and absence of the applied external homogeneous
field for this quantum system are studied. Obtained exact expressions of the
Wigner distribution function are expressed through the Bessel function of the
first kind and Laguerre polynomials. Further, some of the special cases and
limits are discussed in detail.Comment: 10 pages, 9 figure
A relativistic model of the -dimensional singular oscillator
Exactly solvable -dimensional model of the quantum isotropic singular
oscillator in the relativistic configurational -space is proposed. It
is shown that through the simple substitutions the finite-difference equation
for the -dimensional singular oscillator can be reduced to the similar
finite-difference equation for the relativistic isotropic three-dimensional
singular oscillator. We have found the radial wavefunctions and energy spectrum
of the problem and constructed a dynamical symmetry algebra.Comment: 8 pages, accepted for publication in J. Phys.
On the Wigner function of the relativistic finite-difference oscillator in an external field
The phase-space representation for a relativistic linear oscillator in a
homogeneous external field expressed through the finite-difference equation is
constructed. Explicit expressions of the relativistic oscillator Wigner
quasi-distribution function for the stationary states as well as of states of
thermodynamical equilibrium are obtained and their correct limits are shown.Comment: 12 pages, 6 figures, IOP styled LaTeX, to be published in Journal of
Physics
The Relativistic Linear Singular Oscillator
Exactly-solvable model of the linear singular oscillator in the relativistic
configurational space is considered. We have found wavefunctions and energy
spectrum for the model under study. It is shown that they have correct
non-relativistic limits.Comment: 14 pages, 12 figures in eps format, IOP style LaTeX file (revised
taking into account referees suggestions