Related papers: Comment on "Relativistic extension of shape-invari…
In this comment we point out numerous errors in the paper of Alhaidari cited in the title.
We do not think that the relativistic Morse potential problem has been correctly formulated and solved by Alhaidari (Phys. Rev. Lett. 87, 210405 (2001)).
We concur with de Castro's observation that the gauge considerations of our approach are not valid. Nevertheless, except for an error that will be corrected, all of our findings are accurate independent of those considerations.
The points raised in the Comment are addressed and except for one error, which will be corrected, the conclusion is that all of our findings are accurate.
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…
It is proved the equivalence of the compatibility condition of [A. Ramos, J. Phys. A 44 (2011) 342001, Phys. Lett. A 376 (2012) 3499] with a condition found in [Yadav et al., Ann. Phys. 359 (2015) 46]. The link of Shape Invariance with the…
In this comment it is argued that the argument for a unique determination of the electromagnetic potentials in classical electrodynamics in [1] is flawed. To the contrary the "gauge freedom" of the electromagnetic potentials has proven as…
Some issues in relating the central extensions of the planar Galilei group to parameters in the corresponding relativistic theory are discussed.
The usual concept of shape invariance is discussed and one extension of this concept is suggested.
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…
The paper was a preliminary and rejected by the author attempt to describe compact relativistic objects.
We develop a new framework of relative algebroids to address existence and classification problems of geometric structures subject to partial differential equations.
Phenomena in gauge theory are often described in the physics literature via a specific choice of gauge. In foundational and philosophical discussions this is often criticized as introducing gauge dependence, and contrasted against (often…
The basic concepts of factorizable problems in one-dimensional Quantum Mechanics, as well as the theory of Shape Invariant potentials are reviewed. The relation of this last theory with a generalization of the classical Factorization Method…
The apparent impossibility of extending non-relativistic quantum mechanics to a relativistic quantum theory is shown to be due to the insufficient structural richness of the field of complex numbers over which quantum mechanics is built. A…
Irreducible gauge theories in both the Lagrangian and Hamiltonian versions of the Sp(2)-covariant quantization method are studied. Solutions to generating equations are obtained in the form of expansions in power series of ghost and…
The purpose of this article is to draw attention to some fundamental issues in General Relativity. It is argued that these deep issues cannot be resolved within the standard approach to general relativity that considers {\em every} solution…
The exact bound state spectrum of rationally extended shape invariant real as well as $PT$ symmetric complex potentials are obtained by using potential group approach. The generators of the potential groups are modified by introducing a new…
Two complementary approaches to the theory of heavy quarkonia are discussed. The nonrelativistic potential models give amazingly accurate predictions, but lack a theoretical justification. The expansion in powers of $v/c$ is theoretically…
This work is concerned about introducing two new 1D and 3D confined potentials and present their solutions using the Tridiagonal Representation Approach (TRA). The wavefunction is written as a series in terms of square integrable basis…