Related papers: Confluent Second-Order Supersymmetric Quantum Mech…
The diagonalization of the metrical Hamiltonian of a scalar field with an arbitrary coupling with a curvature in N-dimensional homogeneous isotropic space is performed. The energy spectrum of the corresponding quasiparticles is obtained.…
Making use of the first- and second-order algorithms of supersymmetric quantum mechanics (SUSY-QM), we construct quantum mechanical Hamiltonians whose spectra are related to the zeroes of the Riemann Zeta function $\zeta(s)$. Inspired by…
The supersymmetric quantum mechanics of a two-dimensional non-relativistic particle subject to external magnetic and electric fields is studied in a superfield formulation and with the typical non-minimal coupling of (2+1) dimensions. Both…
Frequency conversion in microresonators has revolutionised modern-day nonlinear and quantum optics. Here, we present a theory of the multimode second harmonic generation in microresonators under conditions when the parametric conversion…
We study a motion of quantum particles, whose properties depend on one coordinate so that they can move freely in the perpendicular direction. A rotationally-symmetric Hamiltonian is derived and applied to study a general interface formed…
The energy spectra of two different quantum systems are paired through supersymmetric algorithms. One of the systems is Hermitian and the other is characterized by a complex-valued potential, both of them with only real eigenvalues in their…
Two known 2-dim SUSY quantum mechanical constructions - the direct generalization of SUSY with first-order supercharges and Higher order SUSY with second order supercharges - are combined for a class of 2-dim quantum models, which {\it are…
A transformation of supersymmetric quantum mechanics for N coupled channels is presented, which allows the introduction of up to N degenerate bound states without altering the remaining spectrum of the Hamiltonian. Phase equivalence of the…
We demonstrate that quantum Hamiltonian operator for a free transverse field within the framework of the second quantization reveals an alternative set of states satisfying the eigenstate functional equations. The construction is based upon…
General non-commutative supersymmetric quantum mechanics models in two and three dimensions are constructed and some two and three dimensional examples are explicitly studied. The structure of the theory studied suggest other possible…
The Dunkl Laplacian is used to define the Hamiltonian of a modified quantum harmonic oscillator, associated with any finite reflection group. The potential is a sum of the inverse squares of the linear functions whose zero sets are the…
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…
Quantum mechanics in the presence of $\delta$-function potentials is known to be plagued by UV divergencies which result from the singular nature of the potentials in question. The standard method for dealing with these divergencies is by…
It is shown that the operator methods of supersymmetric quantum mechanics and the concept of shape invariance can profitably be used to derive properties of spherical harmonics in a simple way. The same operator techniques can also be…
We construct supersymmetric quantum mechanics in terms of two real supercharges on noncommutative space in arbitrary dimensions. We obtain the exact eigenspectra of the two and three dimensional noncommutative superoscillators. We further…
The two-nucleon spectral function in nuclear matter is studied using Correlated Basis Function perturbation theory, including central and tensor correlations produceded by a realistic hamiltonian. The factorization property of the…
Among the list of one dimensional solvable Hamiltonians, we find the Hamiltonian with the Rosen--Morse II potential. The first objective is to analyze the scattering matrix corresponding to this potential. We show that it includes a series…
New types of irreducible second order Darboux transformations for the one dimensional Schroedinger equation are described. The main feature of such transformations is that the transformation functions have the eigenvalues grater then the…
Classical particle mechanics on curved spaces is related to the flow of ideal fluids, by a dual interpretation of the Hamilton-Jacobi equation. As in second quantization, the procedure relates the description of a system with a finite…
The quantum Hamiltonian reduction on the OSp(1,2) super Kac-Moody algebra is described in the BRST formalism. Using a free field representation of the KM currents, the super Kac-Moody algebra is shown to be reduced to a superconformal one…