52 research outputs found
Shape Invariance and Its Connection to Potential Algebra
Exactly solvable potentials of nonrelativistic quantum mechanics are known to
be shape invariant. For these potentials, eigenvalues and eigenvectors can be
derived using well known methods of supersymmetric quantum mechanics. The
majority of these potentials have also been shown to possess a potential
algebra, and hence are also solvable by group theoretical techniques. In this
paper, for a subset of solvable problems, we establish a connection between the
two methods and show that they are indeed equivalent.Comment: Latex File, 10 pages, One figure available on request. Appeared in
the proceedings of the workshop on "Supersymmetric Quantum Mechanics and
Integrable Models" held at University of Illinois, June 12-14, 1997; Ed. H.
Aratyn et a
Semi-fermionic representation for spin systems under equilibrium and non-equilibrium conditions
We present a general derivation of semi-fermionic representation for spin
operators in terms of a bilinear combination of fermions in real and imaginary
time formalisms. The constraint on fermionic occupation numbers is fulfilled by
means of imaginary Lagrange multipliers resulting in special shape of
quasiparticle distribution functions. We show how Schwinger-Keldysh technique
for spin operators is constructed with the help of semi-fermions. We
demonstrate how the idea of semi-fermionic representation might be extended to
the groups possessing dynamic symmetries (e.g. singlet/triplet transitions in
quantum dots). We illustrate the application of semi-fermionic representations
for various problems of strongly correlated and mesoscopic physics.Comment: Review article, 40 pages, 11 figure
Supersymmetric Fokker-Planck strict isospectrality
I report a study of the nonstationary one-dimensional Fokker-Planck solutions
by means of the strictly isospectral method of supesymmetric quantum mechanics.
The main conclusion is that this technique can lead to a space-dependent
(modulational) damping of the spatial part of the nonstationary Fokker-Planck
solutions, which I call strictly isospectral damping. At the same time, using
an additive decomposition of the nonstationary solutions suggested by the
strictly isospectral procedure and by an argument of Englefield [J. Stat. Phys.
52, 369 (1988)], they can be normalized and thus turned into physical
solutions, i.e., Fokker-Planck probability densities. There might be
applications to many physical processes during their transient periodComment: revised version, scheduled for PRE 56 (1 August 1997) as a B
The su(1,1) dynamical algebra from the Schr\"odinger ladder operators for N-dimensional systems: hydrogen atom, Mie-type potential, harmonic oscillator and pseudo-harmonic oscillator
We apply the Schr\"odinger factorization to construct the ladder operators
for hydrogen atom, Mie-type potential, harmonic oscillator and pseudo-harmonic
oscillator in arbitrary dimensions. By generalizing these operators we show
that the dynamical algebra for these problems is the Lie algebra.Comment: 10 page
On the 3n+l Quantum Number in the Cluster Problem
It has recently been suggested that an exactly solvable problem characterized
by a new quantum number may underlie the electronic shell structure observed in
the mass spectra of medium-sized sodium clusters. We investigate whether the
conjectured quantum number 3n+l bears a similarity to the quantum numbers n+l
and 2n+l, which characterize the hydrogen problem and the isotropic harmonic
oscillator in three dimensions.Comment: 8 pages, revtex, 4 eps figures included, to be published in
Phys.Rev.A, additional material available at
http://radix2.mpi-stuttgart.mpg.de/koch/Diss
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