Related papers: An Alternate Approach to Transition Potentials
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…
Variational (Rayleigh-Ritz) methods are applied to local quantum field theory. For scalar theories the wave functional is parametrized in the form of a superposition of Gaussians and the expectation value of the Hamiltonian is expressed in…
Supersymmetric models in singular extra dimensional spaces feature prominently in many interesting phenomenological models, including those derived from string theory. In this paper we explicitly derive the low energy theory of…
A mapping is obtained relating radial screened Coulomb systems with low screening parameters to radial anharmonic oscillators in N-dimensional space. Using the formalism of supersymmetric quantum mechanics, it is shown that exact solutions…
The Dirac equation is solved to obtain its approximate bound states for a spin-1/2 particle in the presence of trigonometric Poschl-Teller (tPT) potential including a Coulomb-like tensor interaction with arbitrary spin-orbit quantum number…
Using algebraic tools of supersymmetric quantum mechanics we construct classes of conditionally exactly solvable potentials being the supersymmetric partners of the linear or radial harmonic oscillator. With the help of the raising and…
We connect Quantum Hamilton-Jacobi Theory with supersymmetric quantum mechanics (SUSYQM). We show that the shape invariance, which is an integrability condition of SUSYQM, translates into fractional linear relations among the quantum…
In our previous paper I (del Valle--Turbiner, Int. J. Mod. Phys. A34, 1950143, 2019) it was developed the formalism to study the general $D$-dimensional radial anharmonic oscillator with potential $V(r)= \frac{1}{g^2}\,\hat{V}(gr)$. It was…
In this article we will apply the first- and second-order supersymmetric quantum mechanics to obtain new exactly-solvable real potentials departing from the inverted oscillator potential. This system has some special properties; in…
In the standard formulation of quantum mechanics, one starts by proposing a potential function that models the physical system. The potential is then inserted into the Schr\"odinger equation, which is solved for the wave function, bound…
In paper approach of double complex SUSY-transformations with not coincident complex energies of transformation is developed, allowing to deform given real potential $V_{1}$ with obtaining exact solutions. The explicit solutions of the…
We contemplate the pair of the purely imaginary delta-function potentials on a finite interval with Dirichlet boundary conditions. The two parameter model exhibits nicely the expected quantitative features of the unavoided level crossing…
The asymmetric responses of the system between the external force of right and left directions are called "nonreciprocal". There are many examples of nonreciprocal responses such as the rectification by p-n junction. However, the quantum…
Gamow solutions are used to transform self-adjoint energy operators by means of factorization (supersymmetric) techniques. The transformed non-hermitian operators admit a discrete real spectrum which is occasionally extended by a single…
We show that the formalism of supersymmetric quantum mechanics applied to the solvable elliptic function potentials $V(x) = mj(j+1){sn}^2(x,m)$ produces new exactly solvable one-dimensional periodic potentials.
A simple methodology is suggested for the efficient calculation of certain central potentials having singularities. The generalized pseudospectral method used in this work facilitates {\em nonuniform} and optimal spatial discretization.…
We compare the well known Rayleigh-Ritz variational method (RRVM) with a recently proposed approach based on supersymmetric quantum mechanics and the Gram-Schmidt orthogonalization method (SSQMGS). We apply both procedures to a particular…
A parametrized double-well potential is proposed to address the issue of the impact of shape deformability of some bistable physical systems, on their quantum dynamics and classical statistical mechanics. The parametrized double-well…
A new supersymmetric approach to the analysis of dynamical symmetries for matrix quantum systems is presented. Contrary to standard one dimensional quantum mechanics where there is no role for an additional symmetry due to nondegeneracy,…
The formalism of Supersymmetric Quantum Mechanics supplies a trial wave function to be used in the Variational Method. The screened Coulomb potential is analysed within this approach. Numerical and exact results for energy eigenvalues are…