相关论文: Deformed Shape Invariant Superpotentials in Quantu…

A relation between the deformed Hulth\'en potential and the Eckart one is used to write the bound-state wavefunctions of the former in terms of Jacobi polynomials and to calculate their normalization coefficients. The shape invariance…

All known additive shape invariant superpotentials in nonrelativistic quantum mechanics belong to one of two categories: superpotentials that do not explicitly depend on $\hbar$, and their $\hbar$-dependent extensions. The former group…

Although eigenspectra of one dimensional shape invariant potentials with unbroken supersymmetry are easily obtained, this procedure is not applicable when the parameters in these potentials correspond to broken supersymmetry, since there is…

Shape Invariant potentials in the sense of [Gendenshte\"{\i}n L.\'E., JETP Lett. 38, (1983) 356] which depend on more than two parameters are not know to date. In [Cooper F., Ginocchio J.N. and Khare A., Phys. Rev. {\bf 36 D}, (1987) 2458]…

An algebraic treatment of shape-invariant potentials in supersymmetric quantum mechanics is discussed. By introducing an operator which reparametrizes wave functions, the shape-invariance condition can be related to a oscillator-like…

Recently, Quesne on the one side and on the other side Bougie, Gangopadhyaya and Mallow, have discovered new translational shape invariant potentials not present in previous classifications. By using ordinary B\"acklund--Darboux…

The Shape invariant method has the algebraic structure and its algebras are infinite-dimensional. These algebras are converted into finite-dimensional under conditions. Based on the property of this method we obtain the algebraic structure…

Three sets of exactly solvable one-dimensional quantum mechanical potentials are presented. These are shape invariant potentials obtained by deforming the radial oscillator and the trigonometric/hyperbolic P\"oschl-Teller potentials in…

Shape invariance is an important ingredient of many exactly solvable quantum mechanics. Several examples of shape invariant ``discrete quantum mechanical systems" are introduced and discussed in some detail. They arise in the problem of…

Four new exactly solvable, real and shape-invariant potentials associated with a position-dependent effective mass are generated within the concept of shape-invariant potentials using a specific ansatz for superpotential. The accompanying…

Known shape-invariant potentials for the constant-mass Schrodinger equation are taken as effective potentials in a position-dependent effective mass (PDEM) one. The corresponding shape-invariance condition turns out to be deformed. Its…

We consider two families of extensions of the oscillator in a $d$-dimensional constant-curvature space and analyze them in a deformed supersymmetric framework, wherein the starting oscillator is known to exhibit a deformed shape invariance…

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…

A construction method of infinite families of quasi-exactly solvable position-dependent mass Schr\"odinger equations with known ground and first excited states is proposed in a deformed supersymmetric background. Such families correspond to…

A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. The associated special functions are eigenfunctions of some shape invariant operators. These operators can…

Self-similar potentials generalize the concept of shape-invariance which was originally introduced to explore exactly-solvable potentials in quantum mechanics. In this article it is shown that previously introduced algebraic approach to the…

Quantum Hamilton-Jacobi quantization scheme uses the singularity structure of the potential of a quantum mechanical system to generate its eigenspectrum and eigenfunctions, and its efficacy has been demonstrated for several well known…

In this work we use the deformation procedure and explore the route to obtain distinct field theory models that present similar stability potentials. Starting from systems that interact polynomially or hyperbolically, we use a deformation…

We describe some analogues of quantum potentials arising in fractional or deformed Schroedinger equations.

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…