Related papers: Planarizable Supersymmetric Quantum Toboggans
Among all the PT-symmetric potentials defined on complex coordinate contours C(s), the name "quantum toboggan" is reserved for those whose C(s) winds around a singularity and lives on at least two different Riemann sheets. An enriched menu…
A generalization of the concept of PT-symmetric Hamiltonians H=p^2+V(x) is described. It uses analytic potentials V(x) (with singularities) and a generalized concept of PT-symmetric asymptotic boundary conditions. Nontrivial toboggans are…
The breaking of supersymmetry due to singular potentials in supersymmetric quantum mechanics is critically analyzed. It is shown that, when properly regularized, these potentials respect supersymmetry, even when the regularization parameter…
Supersymmetric quantum mechanics is constructed in a new non-Hermitian representation. Firstly, the map between the partner operators $H^{(\pm)}$ is chosen antilinear. Secondly, both these components of a super-Hamiltonian ${\cal H}$ are…
Witten's supersymmetric quantum mechanics may incorporate potentials with strong singularities after their appropriate regularization. This was proposed by Das and Pernice [Nucl. Phys. B 561 (1999) 357 and arXiv: hep-th/0207112]. We suggest…
The breaking of supersymmetry due to singular potentials in supersymmetric quantum mechanics is critically analyzed. It is shown that, when properly regularized, these potentials respect supersymmetry, even when the regularization parameter…
Certain complex-contour (a.k.a. quantum-toboggan) generalizations of Schroedinger's bound-state problem are reviewed and studied in detail. Our key message is that the practical numerical solution of these atypical eigenvalue problems may…
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…
Within the standard quantum mechanics a q-deformation of the simplest N=2 supersymmetry algebra is suggested. Resulting physical systems do not have conserved charges and degeneracies in the spectra. Instead, superpartner Hamiltonians are…
Even if the motion of a quantum (quasi-)particle proceeds along a left-right-symmetric (PT-symmetric) curved path in complex plane, the spectrum of bound states may remain physical, i.e., real and bounded below). We propose a…
SUSY partnership between singular potentials often breaks down. Via regularization it can be restored on certain ad hoc subspaces of Hilbert space [Das and Pernice, Nucl. Phys. B 561 (1999) 357]. Within the naturally complexified (so called…
Affine transformations (dilatations and translations) are used to define a deformation of one-dimensional $N=2$ supersymmetric quantum mechanics. Resulting physical systems do not have conserved charges and degeneracies in the spectra.…
The Standard Model may be included within a supersymmetric theory, postulating new sparticles that differ by half-a-unit of spin from their standard model partners, and by a new quantum number called R-parity. The lightest one, usually a…
Witten's non-relativistic formalism of supersymmetric quantum mechanics was based on a factorization and partnership between Schroedinger equations. We show how it accommodates a transition to the partnership between relativistic…
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 consider supersymmetric quantum mechanical models with both local and nonlocal potentials. We present a nonlocal deformation of exactly solvable local models. Its energy eigenfunctions and eigenvalues are determined exactly. We observe…
One-dimensional nonrelativistic systems are studied when time-independent potential interactions are involved. Their supersymmetries are determined and their closed subsets generating kinematical invariance Lie superalgebras are pointed…
Supersymmetric quantum mechanics (SUSY QM) is a powerful tool for generating new potentials with known spectra departing from an initial solvable one. In these lecture notes we will present some general formulas concerning SUSY QM of first…
Quantization of the nonlinear supersymmetry faces a problem of a quantum anomaly. For some classes of superpotentials, the integrals of motion admit the corrections guaranteeing the preservation of the nonlinear supersymmetry at the quantum…
Besides the standard quantum version of the Coulomb/Kepler problem, an alternative quantum model with not too dissimilar phenomenological (i.e., spectral and scattering) as well as mathematical (i.e., exact-solvability) properties may be…