16 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
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
Exact solution of the position-dependent effective mass and angular frequency Schr\"odinger equation: harmonic oscillator model with quantized confinement parameter
We present an exact solution of a confined model of the non-relativistic
quantum harmonic oscillator, where the effective mass and the angular frequency
are dependent on the position. The free Hamiltonian of the proposed model has
the form of the BenDaniel--Duke kinetic energy operator. The
position-dependency of the mass and the angular frequency is such that the
homogeneous nature of the harmonic oscillator force constant and hence the
regular harmonic oscillator potential is preserved. As a consequence thereof, a
quantization of the confinement parameter is observed. It is shown that the
discrete energy spectrum of the confined harmonic oscillator with
position-dependent mass and angular frequency is finite, has a non-equidistant
form and depends on the confinement parameter. The wave functions of the
stationary states of the confined oscillator with position-dependent mass and
angular frequency are expressed in terms of the associated Legendre or
Gegenbauer polynomials. In the limit where the confinement parameter tends to
, both the energy spectrum and the wave functions converge to the
well-known equidistant energy spectrum and the wave functions of the stationary
non-relativistic harmonic oscillator expressed in terms of Hermite polynomials.
The position-dependent effective mass and angular frequency also become
constant under this limit
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.
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
Infrared renormalons and single meson production in proton-proton collisions
In this article, we investigate the contribution of the higher twist Feynman
diagrams to the large- inclusive pion production cross section in
proton-proton collisions and present the general formulae for the higher twist
differential cross sections in the case of the running coupling and frozen
coupling approaches. The structure of infrared renormalon singularities of the
higher twist subprocess cross section and the resummed expression (the Borel
sum) for it are found. We compared the resummed higher twist cross sections
with the ones obtained in the framework of the frozen coupling approximation
and leading twist cross section. We obtain, that ratio for all values of
the transverse momentum of the pion identical equivalent to ratio .
It is shown that the resummed result depends on the choice of the meson wave
functions used in calculation. Phenomenological effects of the obtained results
are discussed.Comment: 28 pages, 13 figure
Factorization method for difference equations of hypergeometric type on nonuniform lattices
We study the factorization of the hypergeometric-type difference equation of
Nikiforov and Uvarov on nonuniform lattices. An explicit form of the raising
and lowering operators is derived and some relevant examples are given.Comment: 21 page
Performance of a plastic scintillator developed using styrene monomer polymerization
This paper presents a newly developed plastic scintillator produced in
collaboration with Turkiye Energy, Nuclear and Mineral Research Agency
(TENMAK). The scintillator is manufactured using thermal polymerization of
commercially available styrene monomer. The absorption spectrum of the
scintillator exhibited two absorption bands at 225 nm and 340 nm, with an
absorption edge observed at 410 nm. The wavelength of the emitted light was
measured in the range of 400-800 nm, with a maximum intensity at 427 nm.
Monoenergetic electrons from the 137Cs source were used to evaluate the
characteristics of the new scintillator, particularly its light yield. As the
light readout the MAPD-3NM type silicon photomultiplier array (4 x 4) with an
active area of 15 x 15 mm2, assembled using single MAPDs with an active area of
3.7 x 3.7 mm2, was used. The light yield of the scintillator was determined to
be 6134 photons/MeV. In addition, the efficiency of the scintillator for gamma
rays with an energy of 662 keV was found to be approximately 1.8 %. A CmBe
neutron source was employed to evaluate its fast neutron detection performance.
However, neutron/gamma discrimination using pulse shape discrimination (charge
integration) method was not observed. The results demonstrate the potential of
a newly produced plastic scintillator for various applications, particularly in
radiation monitoring and detection systems.Comment: 7 pages, 7 figure