Related papers: Reply to 'Comment on "Relativistic shape invariant…
We show that the conditional shape invariance symmetry can be used as a very powerful tool to calculate the eigenvalues of the mixed potential V (r) = ar + br^2 +c/r + l(l+1)/r^2 for a restricted set of potential parameters. The energy for…
It is shown that the results of ref [1] are consistent.
Replying to the above Comment by G.Q.Li and R.Machleidt, we point out that the supposed "flaws" in our Comparison of NN potential models with the pp- scattering data [ Phys.Rev.C47,761(1993) ] are in reality not flaws at all.
Using the method of shape invariant potentials, a number of exact solutions of one dimensional effective mass Schrodinger equation are obtained. The solutions with equi-spaced spectrum are discussed in detail.
We formulate the structure of spectral invariance in shape invariance single and double well potentials using derivative invariance.
Rationally extended shape invariant potentials in arbitrary D-dimensions are obtained by using point canonical transformation (PCT) method. The bound-state solutions of these exactly solvable potentials can be written in terms of X_m…
We develop a new approach to build the eigenfunctions of a translationally shape-invariant potential. For this we show that their logarithmic derivatives can be expressed as terminating continued fractions in an appropriate variable. We…
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…
In this paper we investigate the exactness of the WKB quantization condition for translationally shape invariant systems. In particular, using the formalism of supersymmetric quantum mechanics, we generalize the Langer correction and show…
Using the ideas of supersymmetry and shape invariance we show that the eigenvalues and eigenfunctions of a wide class of noncentral potentials can be obtained in a closed form by the operator method. This generalization considerably extends…
The Comments are devoted to the paper ``Solutions of Multitime Reaction-Diffusion PDE'' (Mathematics, vol. 10 (2022), 3623), in which main results are misleading and can be derived in a simple way from those obtained earlier. Moreover, it…
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…
We respond to the accompanying Comment on our paper, 'Validity of certain soft photon amplitudes'. While we hope the discussion here clarifies the issues, we have found nothing which leads to a change in the original conclusions of our…
Combining recent results on rational solutions of the Riccati-Schr\"odinger equations for shape invariant potentials to the scheme developed by Fellows and Smith in the case of the one dimensional harmonic oscillator, we show that it is…
We analyze the supersymmetry and the shape invariance of the potentials of the (1+1) relativistic oscillators we have recently proposed.
A comment has been recently posted on the arXiv (arXiv:1902.07504) that discuss our recent work on encircling multiple exceptional points in Nat. Commun. 9, 4808 (2018). In that comment, the authors claim that our approach is prone to…
The existence of a novel enlarged shape invariance property valid for some rational extensions of shape-invariant conventional potentials, first pointed out in the case of the Morse potential, is confirmed by deriving all rational…
An analytical expression for the relativistic corrections to the energy spectra of particles completely confined in an one-dimensional limited length in real space is given, based upon the wave property of particles, the relativistic…
We show that, contrarily to the claims in [K. Bradler, (2011), arXiv:1108.5553] (and arXiv:1201.1045), the reference [Phys. Rev. A 83, 062323 (2011)] is devoid of flaws or mistakes. We show that the criticism comes from a misunderstanding…
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…