Coherent states for polynomial su(1,1) algebra and a conditionally solvable system

In a previous paper [{\it J. Phys. A: Math. Theor.} {\bf 40} (2007) 11105], we constructed a class of coherent states for a polynomially deformed $su(2)$ algebra. In this paper, we first prepare the discrete representations of the nonlinearly deformed $su(1,1)$ algebra. Then we extend the previous procedure to construct a discrete class of coherent states for a polynomial su(1,1) algebra which contains the Barut-Girardello set and the Perelomov set of the SU(1,1) coherent states as special cases. We also construct coherent states for the cubic algebra related to the conditionally solvable radial oscillator problem.Comment: 2 figure

Supersymmetry of a Nonstationary Pauli Equation

The supersymmetry of the electron in both the nonstationary magnetic and electric fields in a two-dimensional case is studied. The supercharges which are the integrals of motion and their algebra are established. Using the obtained algebra the solutions of nonstationary Pauli equation are generated.Comment: 12 pages, Late

Motion of a spin 1/2 particle in shape invariant scalar and magnetic fields

We study the motion of a spin 1/2 particle in a scalar as well as a magnetic field within the framework of supersymmetric quantum mechanics(SUSYQM). We also introduce the concept of shape invariant scalar and magnetic fields and it is shown that the problem admits exact analytical solutions when such fields are considered.Comment: 14 page

Supersymmetry of the Nonstationary Schr\"odinger equation and Time-Dependent Exactly Solvable Quantum Models

New exactly solvable quantum models are obtained with the help of the supersymmetric extencion of the nonstationary Schr/"odinger equation.Comment: Talk at the 8th International Conference "Symmetry Methods in Physics". Dubna, Russia, 28 July - 2 August, 199

Supersymmetry solution for finitely extensible dumbbell model

Exact relaxation times and eigenfunctions for a simple mechanical model of polymer dynamics are obtained using supersymmetry methods of quantum mechanics. The model includes the finite extensibility of the molecule and does not make use of the self-consistently averaging approximation. The finite extensibility reduces the relaxation times when compared to a linear force. The linear viscoelastic behaviour is obtained in the form of the ``generalized Maxwell model''. Using these results, a numerical integration scheme is proposed in the presence of a given flow kinematics.Comment: 5 pages, 2 figure

Deformed Clifford algebra and supersymmetric quantum mechanics on a phase space with applications in quantum optics

In order to realize supersymmetric quantum mechanics methods on a four dimensional classical phase-space, the complexified Clifford algebra of this space is extended by deforming it with the Moyal star-product in composing the components of Clifford forms. Two isospectral matrix Hamiltonians having a common bosonic part but different fermionic parts depending on four real-valued phase space functions are obtained. The Hamiltonians are doubly intertwined via matrix-valued functions which are divisors of zero in the resulting Moyal-Clifford algebra. Two illustrative examples corresponding to Jaynes-Cummings-type models of quantum optics are presented as special cases of the method. Their spectra, eigen-spinors and Wigner functions as well as their constants of motion are also obtained within the autonomous framework of deformation quantization.Comment: 22 pages. published versio

Coalescing binary systems of compact objects: Dynamics of angular momenta

The end state of a coalescing binary of compact objects depends strongly on the final total mass M and angular momentum J. Since gravitational radiation emission causes a slow evolution of the binary system through quasi-circular orbits down to the innermost stable one, in this paper we examine the corresponding behavior of the ratio J/M^2 which must be less than 1(G/c) or about 0.7(G/c) for the formation of a black hole or a neutron star respectively. The results show cases for which, at the end of the inspiral phase, the conditions for black hole or neutron star formation are not satisfied. The inclusion of spin effects leads us to a study of precession equations valid also for the calculation of gravitational waveforms.Comment: 22 pages, AASTeX and 13 figures in PostScrip

Supersymmetric Method for Constructing Quasi-Exactly and Conditionally-Exactly Solvable Potentials

Using supersymmetric quantum mechanics we develop a new method for constructing quasi-exactly solvable (QES) potentials with two known eigenstates. This method is extended for constructing conditionally-exactly solvable potentials (CES). The considered QES potentials at certain values of parameters become exactly solvable and can be treated as CES ones.Comment: 17 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