4,184 research outputs found
Effective mass in quasi two-dimensional systems
The effective mass of the quasiparticle excitations in quasi two-dimensional
systems is calculated analytically. It is shown that the effective mass
increases sharply when the density approaches the critical one of
metal-insulator transition. This suggests a Mott type of transition rather than
an Anderson like transition.Comment: 3 pages 3 figure
Arbitrary l-state solutions of the rotating Morse potential by the asymptotic iteration method
For non-zero values, we present an analytical solution of the radial
Schr\"{o}dinger equation for the rotating Morse potential using the Pekeris
approximation within the framework of the Asymptotic Iteration Method. The
bound state energy eigenvalues and corresponding wave functions are obtained
for a number of diatomic molecules and the results are compared with the
findings of the super-symmetry, the hypervirial perturbation, the
Nikiforov-Uvarov, the variational, the shifted 1/N and the modified shifted 1/N
expansion methods.Comment: 15 pages with 1 eps figure. accepted for publication in Journal of
Physics A: Mathematical and Genera
Extension of Nikiforov-Uvarov Method for the Solution of Heun Equation
We report an alternative method to solve second order differential equations
which have at most four singular points. This method is developed by changing
the degrees of the polynomials in the basic equation of Nikiforov-Uvarov (NU)
method. This is called extended NU method for this paper. The eigenvalue
solutions of Heun equation and confluent Heun equation are obtained via
extended NU method. Some quantum mechanical problems such as Coulomb problem on
a 3-sphere, two Coulombically repelling electrons on a sphere and hyperbolic
double-well potential are investigated by this method
Low-lying spectra in anharmonic three-body oscillators with a strong short-range repulsion
Three-body Schroedinger equation is studied in one dimension. Its two-body
interactions are assumed composed of the long-range attraction (dominated by
the L-th-power potential) in superposition with a short-range repulsion
(dominated by the (-K)-th-power core) plus further subdominant power-law
components if necessary. This unsolvable and non-separable generalization of
Calogero model (which is a separable and solvable exception at L = K = 2) is
presented in polar Jacobi coordinates. We derive a set of trigonometric
identities for the potentials which generalizes the well known K=2 identity of
Calogero to all integers. This enables us to write down the related partial
differential Schroedinger equation in an amazingly compact form. As a
consequence, we are able to show that all these models become separable and
solvable in the limit of strong repulsion.Comment: 18 pages plus 6 pages of appendices with new auxiliary identitie
Multi-Atomic Mirror for Perfect Reflection of Single Photons in A Wide Band of Frequency
A resonant two level atom doped in one dimensional waveguide behaves as a
mirror, but this single-atom "mirror" can only reflect single photon perfectly
at a specific frequency. For a one dimensional coupled-resonator waveguide, we
propose to extend the perfect reflection region from a specific frequency to a
wide band by placing many atoms individually in the resonators in a finite
coordinate region of the waveguide. Such a doped resonator array promises us to
control the propagation of a practical photon wave packet with certain momentum
distribution instead of a single photon, which is ideally represented by a
plane wave with specific momentum. The studies based on the discrete-coordinate
scattering theory display that such hybrid structure indeed provides a
near-perfect reflection for single photon in a wide band. We also calculated
photon group velocity distribution, which shows that the perfect reflection
with wide band exactly corresponds to the stopping light region.Comment: 8 pages, 10 figure
Polynomial Solutions of Shcrodinger Equation with the Generalized Woods Saxon Potential
The bound state energy eigenvalues and the corresponding eigenfunctions of
the generalized Woods Saxon potential are obtained in terms of the Jacobi
polynomials. Nikiforov Uvarov method is used in the calculations. It is shown
that the results are in a good agreement with the ones obtained before.Comment: 14 pages, 2 figures, submitted to Physical Review
Auxiliary field method and analytical solutions of the Schr\"{o}dinger equation with exponential potentials
The auxiliary field method is a new and efficient way to compute approximate
analytical eigenenergies and eigenvectors of the Schr\"{o}dinger equation. This
method has already been successfully applied to the case of central potentials
of power-law and logarithmic forms. In the present work, we show that the
Schr\"{o}dinger equation with exponential potentials of the form can also be analytically solved by using the
auxiliary field method. Formulae giving the critical heights and the energy
levels of these potentials are presented. Special attention is drawn on the
Yukawa potential and the pure exponential one
Origin of adiabatic and non-adiabatic spin transfer torques in current-driven magnetic domain wall motion
A consistent theory to describe the correlated dynamics of quantum mechanical
itinerant spins and semiclassical local magnetization is given. We consider the
itinerant spins as quantum mechanical operators, whereas local moments are
considered within classical Lagrangian formalism. By appropriately treating
fluctuation space spanned by basis functions, including a zero-mode wave
function, we construct coupled equations of motion for the collective
coordinate of the center-of-mass motion and the localized zero-mode coordinate
perpendicular to the domain wall plane. By solving them, we demonstrate that
the correlated dynamics is understood through a hierarchy of two time scales:
Boltzmann relaxation time when a non-adiabatic part of the spin-transfer torque
appears, and Gilbert damping time when adiabatic part comes up.Comment: 4 pages, 2 figure
Shift of the 2 state of Be in the ternary cold fission of Cf
Recent experimental data indicate that in the ternary cold fission of
Cf the energy of the first excited state of the accompanying light
cluster Be is decreased by an amount ranging between 6 and 26
keV. A model is proposed to calculate the shift of the vibrational 2
state in Be when its heavy companions are the even-even nuclei
Ba and Sr. The stiffness parameters of the -vibrations
are calculated within the self-consistent Hartree-Fock method with BCS pairing
correlations taken into account, and its change is determined by the
interaction of the light cluster with the heavy fragments. The results are
pointing to a dependence of the shift magnitude and signature on the relative
distance between the three clusters and their mutual orientation. Eventually it
is the anharmonic perturbation of the spherical vibrator which is responsible
for obtaining a negative energy shift of the 2 state.Comment: 4 pages, 3 figure
Analytical solutions of the Bohr Hamiltonian with the Morse potential
Analytical solutions of the Bohr Hamiltonian are obtained in the
-unstable case, as well as in an exactly separable rotational case with
, called the exactly separable Morse (ES-M) solution. Closed
expressions for the energy eigenvalues are obtained through the Asymptotic
Iteration Method (AIM), the effectiveness of which is demonstrated by solving
the relevant Bohr equations for the Davidson and Kratzer potentials. All medium
mass and heavy nuclei with known and bandheads have been
fitted by using the two-parameter -unstable solution for transitional
nuclei and the three-parameter ES-M for rotational ones. It is shown that
bandheads and energy spacings within the bands are well reproduced for more
than 50 nuclei in each case.Comment: 33 pages with 2 Tables and 2 Figure
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