Related papers: Multi-Well Potentials in Quantum Mechanics and Sto…
In this paper we investigate the shape invariance property of a potential in one dimension. We show that a simple ansatz allows us to reconstruct all the known shape invariant potentials in one dimension. This ansatz can be easily extended…
Using the method of the "exact discretization" of the Schr\"odinger equation, we propose a particular discretized version of the N=2 Supersymmetric Quantum Mechanics. After defining the corresponding shape invariance condition, we show that…
This article investigates the properties of a few interacting particles trapped in a few wells and how these properties change under adiabatic tuning of interaction strength and inter-well tunneling. While some system properties are…
We construct the $\mathcal{N}=8$ supersymmetric mechanics with potential term whose configuration space is the special K\"ahler manifold of rigid type and show that it can be viewed as the K\"ahler counterpart of $\mathcal{N}=4$ mechanics…
We study quantum mechanics of a massive superparticle in d=4 which preserves 1/4 of the target space supersymmetry with eight supercharges, and so corresponds to the partial breaking N=8 down to N=2. Its worldline action contains a…
We introduce the third five-parametric ordinary hypergeometric energy-independent quantum-mechanical potential, after the Eckart and P\"oschl-Teller potentials, which is proportional to an arbitrary variable parameter and has a shape that…
We present a study of a general spin Hamiltonian with terms up to fourth order. With the coherent states the semiclassical potential is obtained and with catastrophe theory its parameter space is constructed. When the fourth order…
We construct, in the framework of the N=4 SYM theory, a supermultiplet of twist-two conformal operators and study their renormalization properties. The components of the supermultiplet have the same anomalous dimension and enter as building…
We revisit the moduli space approximation to the quantum mechanics of monopoles in N=4 supersymmetric Yang-Mills-Higgs theory with maximal symmetry breaking. Starting with the observation that the set of fermionic zero-modes in N=4…
We construct N=8 supersymmetric mechanics with four bosonic end eight fermionic physical degrees of freedom. Starting from the most general N=4 superspace action in harmonic superspace for the ({\bf 4,8,4}) supermultiplet we find conditions…
Different features of a potential in the form of a Gaussian well have been discussed extensively. Although the details of the calculation are involved, the general approach uses a variational method and WKB approximation, techniques which…
We analyze general structure of N-fold supersymmetry which provides a systematic framework to construct weakly quasi-solvable quantum mechanical systems. Main ingredients of our analysis are dimensional analysis and introduction of an…
In this work we present an introduction to Supersymmetry in the context of 1-dimensional Quantum Mechanics. For that purpose we develop the concept of hamiltonians factorization using the simple harmonic oscillator as an example, we…
The holomorphicity property of N=1 superpotentials or of N=2 F-terms involving vector multiplets is generalized to the case of N=4 1/2-BPS effective operators defined in harmonic superspace. The resulting harmonicity equations are shown to…
An asymmetric double-well potential is considered, assuming that the minima of the wells are quadratic with a frequency $\omega$ and the difference of the minima is close to a multiple of $\hbar \omega$. A WKB wave function is constructed…
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…
A generalized formulation of non-relativistic quantum mechanics is developed within multidimensional geometric (NG) frameworks characterized by a power-law dispersion relation \(E \propto |p|^{j}\), where \(j = N - 1\). Starting from the…
Intervalley mixing between conduction-band states in low-dimensional Si/SiGe heterostructures induces splitting between nominally degenerate energy levels. The symmetric double-valley effective mass approximation and the empirical…
We construct N=4 supersymmetric mechanics using the N=4 nonlinear chiral supermultiplet. The two bosonic degrees of freedom of this supermultiplet parameterize the sphere S(2) and go into the bosonic components of the standard chiral…
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…