Related papers: Wronskian formula for confluent second-order super…
In this paper, we revisit the well known Bohr-Sommerfeld quantization rule (BS) of order 2 for a self-adjoint 1-D semiclassical pseudo-differential operator, within the algebraic and microlocal framework of B. Helffer and J. Sj\"{o}strand.…
We have re-analyzed the dynamics of the thermal potential within Schwarzschild spacetime by employing the Fokker-Planck equation. We demonstrate that the Fokker-Planck equation reduces to a simplified form equivalent to a scaled quantum…
Supersymmetric quantum mechanics has many applications, and typically uses a raising and lowering operator formalism. For one dimensional problems, we show how such raising and lowering operators may be generalized to include an arbitrary…
General formulas of the two-electron operator representing either atomic or effective interactions are given in a coupled tensorial form in relativistic approximation. The alternatives of using uncoupled, coupled and antisymmetric…
Systematic iterative algorithms of supersymmetric quantum mechanics (SUSYQM) type for solving the eigenequation of principal hypergeometric-like differential operator (HLDO) and for generating the eigenequation of associated HLDO itself as…
Recently the authors and J.M. Kress presented a special function recurrence relation method to prove quantum superintegrability of an integrable 2D system that included explicit constructions of higher order symmetries and the structure…
The Foldy-Wouthuysen transformation for relativistic spin-1 particles interacting with nonuniform electric and uniform magnetic fields is performed. The Hamilton operator in the Foldy-Wouthuysen representation is determined. It agrees with…
In this work we introduce the class of quantum mechanics superpotentials $W(x)=g\epsilon(x) x^{2n}$ and study in details the cases $n=0$ and 1. The $n=0$ superpotential is shown to lead to the known problem of two supersymmetrically related…
We consider the time-independent Wigner functions of phase-space quantum mechanics (a.k.a. deformation quantization) for a Morse potential. First, we find them by solving the $\ast$-eigenvalue equations, using a method that can be applied…
We compute the $\mathcal{N}=2$ SUSY algebra of the massive Grassmannian sigma model in 2+1 dimensions. We first rederive the action of the model by using the Scherk-Schwarz dimensional reduction from $\mathcal{N}=1$ theory in 3+1…
This paper addresses an investigation on a factorization method for difference equations. It is proved that some classes of second order linear difference operators, acting in Hilbert spaces, can be factorized using a pair of mutually…
The factorization technique for superintegrable Hamiltonian systems is revisited and applied in order to obtain additional (higher-order) constants of the motion. In particular, the factorization approach to the classical anisotropic…
Within the context of Supersymmetric Quantum Mechanics and its related hierarchies of integrable quantum Hamiltonians and potentials, a general programme is outlined and applied to its first two simplest illustrations. Going beyond the…
We extend recent work by Tremblay, Turbiner, and Winternitz which analyzes an infinite family of solvable and integrable quantum systems in the plane, indexed by the positive parameter k. Key components of their analysis were to demonstrate…
We solve the quantum mechanical problem of a charged particle on S^2 in the background of a magnetic monopole for both bosonic and supersymmetric cases by constructing Hilbert space and realizing the fundamental operators obeying…
In the framework of SUSYQM extended to deal with non-Hermitian Hamiltonians, we analyze three sets of complex potentials with real spectra, recently derived by a potential algebraic approach based upon the complex Lie algebra sl(2, C). This…
Since the ($\beta$-deformed) Hurwitz Kontsevich model corresponds to the special case of affine Yangian of ${\mathfrak{gl}}(1)$. In this paper, we construct two general cases of the $\beta$-deformed Hurwitz Kontsevich model. We find that…
Following a letter by Bassett, we show first that it is possible to find an analytical approximation to the error function in terms of a finite series of hyperbolic tangents from the supersymmetric (SUSY) solution of the Poschl-Teller…
We have studied the underlying algebraic structure of the anharmonic oscillator by using the variational perturbation theory. To the first order of the variational perturbation, the Hamiltonian is found to be factorized into a…
Relativistic arbitrary spin Hamiltonians are shown to obey the algebraic structure of supersymmetric quantum system if their odd and even parts commute. This condition is identical to that required for the exactness of the Foldy-Wouthuysen…