160 research outputs found
Accurate calculation of resonances in multiple-well oscillators
Quantum--mechanical multiple--well oscillators exhibit curious complex
eigenvalues that resemble resonances in models with continuum spectra. We
discuss a method for the accurate calculation of their real and imaginary
parts
The optimized Rayleigh-Ritz scheme for determining the quantum-mechanical spectrum
The convergence of the Rayleigh-Ritz method with nonlinear parameters
optimized through minimization of the trace of the truncated matrix is
demonstrated by a comparison with analytically known eigenstates of various
quasi-solvable systems. We show that the basis of the harmonic oscillator
eigenfunctions with optimized frequency ? enables determination of boundstate
energies of one-dimensional oscillators to an arbitrary accuracy, even in the
case of highly anharmonic multi-well potentials. The same is true in the
spherically symmetric case of V (r) = {\omega}2r2 2 + {\lambda}rk, if k > 0.
For spiked oscillators with k < -1, the basis of the pseudoharmonic oscillator
eigenfunctions with two parameters ? and {\gamma} is more suitable, and
optimization of the latter appears crucial for a precise determination of the
spectrum.Comment: 22 pages,8 figure
A model for single electron decays from a strongly isolated quantum dot
Recent measurements of electron escape from a non-equilibrium charged quantum
dot are interpreted within a 2D separable model. The confining potential is
derived from 3D self-consistent Poisson-Thomas-Fermi calculations. It is found
that the sequence of decay lifetimes provides a sensitive test of the confining
potential and its dependence on electron occupation.Comment: 9 pages, 10 figure
Variational collocation for systems of coupled anharmonic oscillators
We have applied a collocation approach to obtain the numerical solution to
the stationary Schr\"odinger equation for systems of coupled oscillators. The
dependence of the discretized Hamiltonian on scale and angle parameters is
exploited to obtain optimal convergence to the exact results. A careful
comparison with results taken from the literature is performed, showing the
advantages of the present approach.Comment: 14 pages, 10 table
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
Convergence of the Gaussian Expansion Method in Dimensionally Reduced Yang-Mills Integrals
We advocate a method to improve systematically the self-consistent harmonic
approximation (or the Gaussian approximation), which has been employed
extensively in condensed matter physics and statistical mechanics. We
demonstrate the {\em convergence} of the method in a model obtained from
dimensional reduction of SU() Yang-Mills theory in dimensions. Explicit
calculations have been carried out up to the 7th order in the large-N limit,
and we do observe a clear convergence to Monte Carlo results. For the convergence is already achieved at the 3rd order, which suggests that
the method is particularly useful for studying the IIB matrix model, a
conjectured nonperturbative definition of type IIB superstring theory.Comment: LaTeX, 4 pages, 5 figures; title slightly changed, explanations added
(16 pages, 14 figures), final version published in JHE
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
Effective-mass Klein-Gordon Equation for non-PT/non-Hermitian Generalized Morse Potential
The one-dimensional effective-mass Klein-Gordon equation for the real, and
non-\textrm{PT}-symmetric/non-Hermitian generalized Morse potential is solved
by taking a series expansion for the wave function. The energy eigenvalues, and
the corresponding eigenfunctions are obtained. They are also calculated for the
constant mass case.Comment: 14 page
A class of nonlinear wave equations containing the continuous Toda case
We consider a nonlinear field equation which can be derived from a binomial
lattice as a continuous limit. This equation, containing a perturbative
friction-like term and a free parameter , reproduces the Toda case (in
absence of the friction-like term) and other equations of physical interest, by
choosing particular values of . We apply the symmetry and the
approximate symmetry approach, and the prolongation technique. Our main purpose
is to check the limits of validity of different analytical methods in the study
of nonlinear field equations. We show that the equation under investigation
with the friction-like term is characterized by a finite-dimensional Lie
algebra admitting a realization in terms of boson annhilation and creation
operators. In absence of the friction-like term, the equation is linearized and
connected with equations of the Bessel type. Examples of exact solutions are
displayed, and the algebraic structure of the equation is discussed.Comment: Latex file + [equations.sty], 22 p
High orders of the perturbation theory for hydrogen atom in magnetic field
The states of hydrogen atom with principal quantum number and zero
magnetic quantum number in constant homogeneous magnetic field are
considered. The coefficients of energy eigenvalues expansion up to 75th order
in powers of are obtained for these states. The series for energy
eigenvalues and wave functions are summed up to values of the order
of atomic magnetic field. The calculations are based on generalization of the
moment method, which may be used in other cases of the hydrogen atom
perturbation by a polynomial in coordinates potential.Comment: 16 pages, LaTeX, 6 figures (ps, eps
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