Related papers: Supersymmetric partners of the trigonometric Posch…
In this work the supersymmetric technique is applied to the truncated oscillator to generate Hamiltonians ruled by second and third-order polynomial Heisenberg algebras, which are connected to the Painlev\'e IV and Painlev\'e V equations…
Constructing the operators connecting the state of energy associated with super partner Hamiltonians and super partner potentials for a linear harmonic oscillator has been discussed and it is shown that any super symmetric eigen state of…
We show that supersymmetry is a simple but powerful tool to exactly solve quantum mechanics problems. Here, the supersymmetric approach is used to analyse a quantum system with periodic P\"oschl-Teller potential, and to find out the exact…
We show that Calogero-Sutherland models for interacting particles have a natural supersymmetric extension. For the construction, we use Jacobians which appear in certain superspaces. Some of the resulting Hamiltonians have a direct physics…
We generalize the standard first-order intertwining relationship of supersymmetric quantum mechanics in order to include simultaneous scaling transformations in both the original Hamiltonian and the intertwining operator. It is argued that…
We extend the study of supersymmetric tridiagonal Hamiltonians to the case of non-Hermitian Hamiltonians with real or complex conjugate eigenvalues. We find the relation between matrix elements of the non-Hermitian Hamiltonian $H$ and its…
The most general Dirac Hamiltonians in $(1+1)$ dimensions are revisited under the requirement to exhibit a supersymmetric structure. It is found that supersymmetry allows either for a scalar or a pseudo-scalar potential. Their spectral…
Supersymmetric quantum mechanics is a powerful tool for generating exactly solvable potentials departing from a given initial one. If applied to the harmonic oscillator, a family of Hamiltonians ruled by polynomial Heisenberg algebras is…
Supersymmetry allows one to build a hierarchy of Hamiltonians that share the same spectral properties and which are pairwise connected through common superpotentials. The iso-spectral properties of these Hamiltonians imply that the dynamics…
The asymptotic behaviour of the superpotential of general SUSY transformations for a coupled-channel Hamiltonian with different thresholds is analyzed. It is shown that asymptotically the superpotential can tend to a diagonal matrix with an…
Second order supersymmetric approach is taken to the system describing motion of a quantum particle in a potential endowed with position-dependent effective mass. It is shown that the intertwining relations between second order partner…
New non Hermitian Hamiltonians are generated, as isospectral partners of the generalized Swanson model, viz., $ H_- = {\cal{A}}^{\dagger} {\cal{A}} + \alpha {\cal{A}} ^2 + \beta {\cal{A}}^{\dagger 2} $, where $ \alpha \beta $ are real…
Fractional supersymmetric quantum mechanics is developed from a generalized Weyl-Heisenberg algebra. The Hamiltonian and the supercharges of fractional supersymmetric dynamical systems are built in terms of the generators of this algebra.…
The main result of this article is that we show that from supersymmetry we can generate new superintegrable Hamiltonians. We consider a particular case with a third order integral and apply the Mielnik's construction in supersymmetric…
We analyze the supersymmetry and the shape invariance of the potentials of the (1+1) relativistic oscillators we have recently proposed.
In this project, we will develop the foundations of quantum mechanics using the methods of supersymmetry. We will discuss the use of the superpotential to derive the supersymmetric partner of a potential in one dimension, and explore…
We extend the standard intertwining relations used in Supersymmetrical (SUSY) Quantum Mechanics which involve real superpotentials to complex superpotentials. This allows to deal with a large class of non-hermitean Hamiltonians and to study…
We study the quantum cosmology of supersymmetric, homogeneous and isotropic, higher derivative models. We recall superfield actions obtained in previous works and give classically equivalent actions leading to second order equations for the…
The problem of finding superintegrable Hamiltonians and their integrals of motion can be reduced to solving a series of compatibility equations that result from the overdetermination of the commutator or Poisson bracket relations. The…
For any odd $k$, a connection is established between the dihedral and supersymmetric extensions of the Tremblay-Turbiner-Winternitz Hamiltonians $H_k$ on a plane. For this purpose, the elements of the dihedral group $D_{2k}$ are realized in…