202 research outputs found
Asymptotic iteration method for eigenvalue problems
An asymptotic interation method for solving second-order homogeneous linear
differential equations of the form y'' = lambda(x) y' + s(x) y is introduced,
where lambda(x) \neq 0 and s(x) are C-infinity functions. Applications to
Schroedinger type problems, including some with highly singular potentials, are
presented.Comment: 14 page
A basis for variational calculations in d dimensions
In this paper we derive expressions for matrix elements (\phi_i,H\phi_j) for
the Hamiltonian H=-\Delta+\sum_q a(q)r^q in d > 1 dimensions.
The basis functions in each angular momentum subspace are of the form
phi_i(r)=r^{i+1+(t-d)/2}e^{-r^p/2}, i >= 0, p > 0, t > 0. The matrix elements
are given in terms of the Gamma function for all d. The significance of the
parameters t and p and scale s are discussed. Applications to a variety of
potentials are presented, including potentials with singular repulsive terms of
the form b/r^a, a,b > 0, perturbed Coulomb potentials -D/r + B r + Ar^2, and
potentials with weak repulsive terms, such as -g r^2 + r^4, g > 0.Comment: 22 page
Perturbation expansions for a class of singular potentials
Harrell's modified perturbation theory [Ann. Phys. 105, 379-406 (1977)] is
applied and extended to obtain non-power perturbation expansions for a class of
singular Hamiltonians H = -D^2 + x^2 + A/x^2 + lambda/x^alpha, (A\geq 0, alpha
> 2), known as generalized spiked harmonic oscillators. The perturbation
expansions developed here are valid for small values of the coupling lambda >
0, and they extend the results which Harrell obtained for the spiked harmonic
oscillator A = 0. Formulas for the the excited-states are also developed.Comment: 23 page
Tempo de tunelamento de um pacote de ondas gaussiano na região de uma barreira de potencial retangular
Dentro da temática do tempo de tunelamento, utilizando o método da fase estacionária, examinamos o tempo de trânsito de um pacote de ondas na região de uma barreira de potencial retangular. O pacote de ondas incidente é construído a partir de uma distribuição gaussiana de momentos. O tempo de trânsito obtido é livre das contribuições devidas às perturbações causadas pelas interferências na região imediatamente anterior à barreira de potencial. Mede o tempo de propagação do pacote de ondas através da região do potencial a partir da sua emergência no início da barreira até a sua chegada ao final da mesma, dentro dos procedimentos do método da fase estacionária
Mechanisms driving alteration of the Landau state in the vicinity of a second-order phase transition
The rearrangement of the Fermi surface of a homogeneous Fermi system upon
approach to a second-order phase transition is studied at zero temperature. The
analysis begins with an investigation of solutions of the equation
, a condition that ordinarily has the Fermi momentum as
a single root. The emergence of a bifurcation point in this equation is found
to trigger a qualitative alteration of the Landau state, well before the
collapse of the collective degree of freedom that is responsible for the
second-order transition. The competition between mechanisms that drive
rearrangement of the Landau quasiparticle distribution is explored, taking into
account the feedback of the rearrangement on the spectrum of critical
fluctuations. It is demonstrated that the transformation of the Landau state to
a new ground state may be viewed as a first-order phase transition.Comment: 16 pages, 10 figure
Perurbation expansions for the spiked harmonic oscillator and related series involving the gamma function
We study weak-coupling perturbation expansions for the ground-state energy of
the Hamiltonian with the generalized spiked harmonic oscillator potential V(x)
= Bx^2 + A/x^2 + lambda/x^alpha, and also for the bottoms of the angular
momentum subspaces labelled by ell = 0,1,2 ..., in N-dimensions corresponding
to the spiked harmonic oscillator potential: V(x) = x^2 + lambda/x^alpha, where
alpha is a real positive parameter. A method of Znojil is then applied to
obtain closed form expressions for the sums of some infinite series whose terms
involve ratios and products of gamma functions.Comment: 9 page
Ground-State of Charged Bosons Confined in a Harmonic Trap
We study a system composed of N identical charged bosons confined in a
harmonic trap. Upper and lower energy bounds are given. It is shown in the
large N limit that the ground-state energy is determined within an accuracy of
and that the mean field theory provides a reasonable result with
relative error of less than 16% for the binding energy .Comment: 15 page
Adaptation of the Landau-Migdal Quasiparticle Pattern to Strongly Correlated Fermi Systems
A quasiparticle pattern advanced in Landau's first article on Fermi liquid
theory is adapted to elucidate the properties of a class of strongly correlated
Fermi systems characterized by a Lifshitz phase diagram featuring a quantum
critical point (QCP) where the density of states diverges. The necessary
condition for stability of the Landau Fermi Liquid state is shown to break down
in such systems, triggering a cascade of topological phase transitions that
lead, without symmetry violation, to states with multi-connected Fermi
surfaces. The end point of this evolution is found to be an exceptional state
whose spectrum of single-particle excitations exhibits a completely flat
portion at zero temperature. Analysis of the evolution of the temperature
dependence of the single-particle spectrum yields results that provide a
natural explanation of classical behavior of this class of Fermi systems in the
QCP region.Comment: 26 pages, 14 figures. Dedicated to 100th anniversary of A.B.Migdal
birthda
Spiked oscillators: exact solution
A procedure to obtain the eigenenergies and eigenfunctions of a quantum
spiked oscillator is presented. The originality of the method lies in an
adequate use of asymptotic expansions of Wronskians of algebraic solutions of
the Schroedinger equation. The procedure is applied to three familiar examples
of spiked oscillators
- …