26 research outputs found

### Self-Similar Potentials and q-Coherent States

The self-similar potentials are formulated in terms of the shape-invariance.
Based on it, a coherent state associated with the shape-invariant potentials is
calculated in case of the self-similar potentials. It is shown that it reduces
to the q-deformed coherent state.Comment: 9 pages, Revtex, preprint YITP/K-103

### Helicity supersymmetry of dyons

The 'dyon' system of D'Hoker and Vinet consisting of a spin 1/2 particle with
anomalous gyromagnetic ratio 4 in the combined field of a Dirac monopole plus a
Coulomb plus a suitable $1/r^2$ potential (which arises in the long-range limit
of a self-dual monopole) is studied following Biedenharn's approach to the
Dirac-Coulomb problem: the explicit solution is obtained using the
`Biedenharn-Temple operator', $\Gamma$, and the extra two-fold degeneracy is
explained by the subtle supersymmetry generated by the 'Dyon Helicity' or
generalized `Biedenharn-Johnson-Lippmann' operator ${\cal R}$. The new SUSY
anticommutes with the chiral SUSY discussed previously.Comment: 14 pages, 2 figure

### Shape-invariant potentials and an associated coherent state

An algebraic treatment of shape-invariant potentials in supersymmetric
quantum mechanics is discussed. By introducing an operator which reparametrizes
wave functions, the shape-invariance condition can be related to a
oscillator-like algebra. It makes possible to define a coherent state
associated with the shape-invariant potentials. For a large class of such
potentials, it is shown that the introduced coherent state has the property of
resolution of unity.Comment: 11 pages + 1 figure (not included),Plain Tex YITP/K-1019, RCNP-05

### Systems with Higher-Order Shape Invariance: Spectral and Algebraic Properties

We study a complex intertwining relation of second order for Schroedinger
operators and construct third order symmetry operators for them. A modification
of this approach leads to a higher order shape invariance. We analyze with
particular attention irreducible second order Darboux transformations which
together with the first order act as building blocks. For the third order
shape-invariance irreducible Darboux transformations entail only one sequence
of equidistant levels while for the reducible case the structure consists of up
to three infinite sequences of equidistant levels and, in some cases, singlets
or doublets of isolated levels.Comment: 18 pages, LaTeX, editorial page is remove

### Isospectrality of spherical MHD dynamo operators: pseudo-Hermiticity and a no-go theorem

The isospectrality problem is studied for the operator of the spherical
hydromagnetic alpha^2-dynamo. It is shown that this operator is formally
pseudo-Hermitian (J-symmetric) and lives in a Krein space. Based on the
J-symmetry, an operator intertwining Ansatz with first-order differential
intertwining operators is tested for its compatibility with the structure of
the alpha^2-dynamo operator matrix. An intrinsic structural inconsistency is
obtained in the set of associated matrix Riccati equations. This inconsistency
is interpreted as a no-go theorem which forbids the construction of isospectral
alpha^2-dynamo operator classes with the help of first-order differential
intertwining operators.Comment: 13 pages, LaTeX2e, improved references, to appear in J. Math. Phy

### A Generalization of the Bargmann-Fock Representation to Supersymmetry by Holomorphic Differential Geometry

In the Bargmann-Fock representation the coordinates $z^i$ act as bosonic
creation operators while the partial derivatives $\partial_{z^j}$ act as
annihilation operators on holomorphic $0$-forms as states of a $D$-dimensional
bosonic oscillator. Considering also $p$-forms and further geometrical objects
as the exterior derivative and Lie derivatives on a holomorphic ${\bf C}^D$, we
end up with an analogous representation for the $D$-dimensional supersymmetric
oscillator. In particular, the supersymmetry multiplet structure of the Hilbert
space corresponds to the cohomology of the exterior derivative. In addition, a
1-complex parameter group emerges naturally and contains both time evolution
and a homotopy related to cohomology. Emphasis is on calculus.Comment: 11 pages, LaTe

### The Spectrum of Sl(2, R)/U(1) Black Hole Conformal Field Theory

We study string theory in the background of a two-dimensional black hole
which is described by an $SL(2, R)/U(1)$ coset conformal field theory. We
determine the spectrum of this conformal field theory using supersymmetric
quantum mechanics and give an explicit form of the vertex operators in terms of
the Jacobi functions. We also discuss the applicability of SUSY quantum
mechanics techniques to non-linear $\sigma$-models.Comment: 21 page

### Multiparticle SUSY quantum mechanics and the representations of permutation group

The method of multidimensional SUSY Quantum Mechanics is applied to the
investigation of supersymmetrical N-particle systems on a line for the case of
separable center-of-mass motion. New decompositions of the superhamiltonian
into block-diagonal form with elementary matrix components are constructed.
Matrices of coefficients of these minimal blocks are shown to coincide with
matrices of irreducible representations of permutations group S_N, which
correspond to the Young tableaux (N-M,1^M). The connections with known
generalizations of N-particle Calogero and Sutherland models are established.Comment: 20 pages, Latex,no figure

### SUSY approach to Pauli Hamiltonians with an axial symmetry

A two-dimensional Pauli Hamiltonian describing the interaction of a neutral
spin-1/2 particle with a magnetic field having axial and second order
symmetries, is considered. After separation of variables, the one-dimensional
matrix Hamiltonian is analyzed from the point of view of supersymmetric quantum
mechanics. Attention is paid to the discrete symmetries of the Hamiltonian and
also to the Hamiltonian hierarchies generated by intertwining operators. The
spectrum is studied by means of the associated matrix shape-invariance. The
relation between the intertwining operators and the second order symmetries is
established and the full set of ladder operators that complete the dynamical
algebra is constructed.Comment: 18 pages, 3 figure

### New Two-Dimensional Quantum Models Partially Solvable by Supersymmetrical Approach

New solutions for second-order intertwining relations in two-dimensional SUSY
QM are found via the repeated use of the first order supersymmetrical
transformations with intermediate constant unitary rotation. Potentials
obtained by this method - two-dimensional generalized P\"oschl-Teller
potentials - appear to be shape-invariant. The recently proposed method of
$SUSY-$separation of variables is implemented to obtain a part of their
spectra, including the ground state. Explicit expressions for energy
eigenvalues and corresponding normalizable eigenfunctions are given in analytic
form. Intertwining relations of higher orders are discussed.Comment: 21 pages. Some typos corrected; imrovements added in Subsect.4.2;
some references adde