Related papers: Comment on 'Relativistic shape invariant potential…

The paper comments on "Quantifying long-term scientific impact". It indicates that there is a mistake of [D. S. Wang , C. Song, A. L. Barabasi, Quantifying long-term scientific impact, Science 342, 127 (2013), arXiv:1306.3293].

Exactly solvable potentials of nonrelativistic quantum mechanics are known to be shape invariant. For these potentials, eigenvalues and eigenvectors can be derived using well known methods of supersymmetric quantum mechanics. The majority…

We show that the basic results on the paper referred in the title [J. Phys. A: Math. Gen. v. 35 (2002) 5333-5345], concerning the derivation of the Ermakov invariant from Noether symmetry methods, are not new.

The above comment [E. I. Lashin, D. Dou, arXiv:1606.04738] claims that the paper "Quantum Raychaudhuri Equation" by S. Das, Phys. Rev. D89 (2014) 084068 [arXiv:1404.3093] has "problematic points" with regards to its derivation and…

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…

Quantum mechanical potentials satisfying the property of shape invariance are well known to be algebraically solvable. Using a scaling ansatz for the change of parameters, we obtain a large class of new shape invariant potentials which are…

We introduce concept of next generation shape invariance and show that the process of shape invariant extension can be continued indefinitely.

A number of authors have recently pointed out inconsistencies of results obtained with the Huang-Yang multipolar pseudo-potential for low-energy scattering [K. Huang and K. C. Yang, Phys. Rev. A, v 105, 767 (1957); later revised in K.…

We show that results obtained in paper Foundations of Physics 33, No. 7, 1107 (2003), are not correct.

We correct a sign mistake in the work mentioned in the title; explore consequences on energy conditions in the relevant context, and make a suggestion on the introduced parameter.

Critical remarks in respect to the Generalized Relativistic Effective Core Potential in the recent article of S.A.Wildman at al. are discussed and shown to be incorrect.

We derive and discuss the constraints induced by Poincare' invariance on the form of the heavy-quark potential up to order 1/m^2. We present two derivations: one uses general arguments directly based on the Poincare' algebra and the other…

This note corrects some omissions in section 2 of the paper "Lipschitz connectivity and filling invariants in solvable groups and buildings."

It is shown that for a class of position dependent mass Schroedinger equation the shape invariance condition is equivalent to a potential symmetry algebra. Explicit realization of such algebras have been obtained for some shape invariant…

This article is a thorough critique to the Weniger's comments made to our papers published in prestigious journals in the recent years. A detailed and critical examination of the arguments that led to the suggested comment by Weniger…

The calculation presented in "A neoclassical calculation of rotation profiles and comparison with DIII-D measurements" by Stacey, Johnson, and Mandrekas, [Physics of Plasmas, 13, (2006)], contains several errors, including the neglect of…

There is a mathematical error in the first version of this paper. A new corrected version will be posted when the error is fixed, possibly with a modified title.

We formulate the structure of spectral invariance in shape invariance single and double well potentials using derivative invariance.

This paper is superseded by arXiv:1106.3363.

This is the article with the same title which is scheduled to appear in the January 2022 issue of the AMS Notices, with additional references which could not be provided in the accepted version due to space constraints. The figures in this…