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