30 research outputs found
Two Electrons in a Quantum Dot: A Unified Approach
Low-lying energy levels of two interacting electrons confined in a
two-dimensional parabolic quantum dot in the presence of an external magnetic
field have been revised within the frame of a novel model. The present
formalism, which gives closed algebraic solutions for the specific values of
magnetic field and spatial confinement length, enables us to see explicitly
individual effects of the electron correlation.Comment: 14 page
First-order intertwining operators and position-dependent mass Schrodinger equations in d dimensions
The problem of d-dimensional Schrodinger equations with a position-dependent
mass is analyzed in the framework of first-order intertwining operators. With
the pair (H, H_1) of intertwined Hamiltonians one can associate another pair of
second-order partial differential operators (R, R_1), related to the same
intertwining operator and such that H (resp. H_1) commutes with R (resp. R_1).
This property is interpreted in superalgebraic terms in the context of
supersymmetric quantum mechanics (SUSYQM). In the two-dimensional case, a
solution to the resulting system of partial differential equations is obtained
and used to build a physically-relevant model depicting a particle moving in a
semi-infinite layer. Such a model is solved by employing either the
commutativity of H with some second-order partial differential operator L and
the resulting separability of the Schrodinger equation or that of H and R
together with SUSYQM and shape-invariance techniques. The relation between both
approaches is also studied.Comment: 25 pages, no figure, 1 paragraph added in section 4, 1 additional
referenc
Spectrum generating algebras for position-dependent mass oscillator Schrodinger equations
The interest of quadratic algebras for position-dependent mass Schr\"odinger
equations is highlighted by constructing spectrum generating algebras for a
class of d-dimensional radial harmonic oscillators with and a
specific mass choice depending on some positive parameter . Via some
minor changes, the one-dimensional oscillator on the line with the same kind of
mass is included in this class. The existence of a single unitary irreducible
representation belonging to the positive-discrete series type for and
of two of them for d=1 is proved. The transition to the constant-mass limit
is studied and deformed su(1,1) generators are constructed.
These operators are finally used to generate all the bound-state wavefunctions
by an algebraic procedure.Comment: 21 pages, no figure, 2 misprints corrected; published versio
Solution of the Dirac equation with position-dependent mass in the Coulomb field
We obtain exact solution of the Dirac equation for a charged particle with
position-dependent mass in the Coulomb field. The effective mass of the spinor
has a relativistic component which is proportional to the square of the Compton
wavelength and varies as 1/r. It is suggested that this model could be used as
a tool in the renormalization of ultraviolet divergences in field theory. The
discrete energy spectrum and spinor wave-function are obtained explicitly.Comment: 6 page
Pseudo-Hermitian versus Hermitian position-dependent-mass Hamiltonians in a perturbative framework
We formulate a systematic algorithm for constructing a whole class of
Hermitian position-dependent-mass Hamiltonians which, to lowest order of
perturbation theory, allow a description in terms of PT-symmetric Hamiltonians.
The method is applied to the Hermitian analogue of the PT-symmetric cubic
anharmonic oscillator. A new example is provided by a Hamiltonian
(approximately) equivalent to a PT-symmetric extension of the one-parameter
trigonometric Poschl-Teller potential.Comment: 13 pages, no figure, modified presentation, 6 additional references,
published versio
A general scheme for the effective-mass Schrodinger equation and the generation of the associated potentials
A systematic procedure to study one-dimensional Schr\"odinger equation with a
position-dependent effective mass (PDEM) in the kinetic energy operator is
explored. The conventional free-particle problem reveals a new and interesting
situation in that, in the presence of a mass background, formation of bound
states is signalled. We also discuss coordinate-transformed, constant-mass
Schr\"odinger equation, its matching with the PDEM form and the consequent
decoupling of the ambiguity parameters. This provides a unified approach to
many exact results known in the literature, as well as to a lot of new ones.Comment: 16 pages + 1 figure; minor changes + new "free-particle" problem;
version published in Mod. Phys. Lett.