Related papers: Reply to 'Comment on "Relativistic shape invariant…
We explain the exact meaning of a statement we made in a previous paper on invariants, namely that a complex-valued function of the data of the functional equation of an $L$-function is an invariant if and only if it is stable under the…
We investigate two methods of obtaining exactly solvable potentials with analytic forms.
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]…
In this note we discuss how several results characterizing the qualitative behavior of solutions to the nonlinear Poisson equation can be generalized to harmonic maps with potential between complete Riemannian manifolds. This includes…
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…
We comment on Z. D. Zhang's Response [arXiv:0812.2330] to our recent Comment [arXiv:0811.3876] addressing the conjectured solution of the three-dimensional Ising model reported in [arXiv:0705.1045].
In our comment we show that some of the very difficult problems have been successfully solved. We have to focus on the resolved problems, since the authors claims: Our hope, however, is that the topics we have presented will provide…
A reference has been corrected
It is shown that the principal results of a recent work by Khalilov are incorrect. These errors are attributable to the author's insistence that wave functions must be regular at the origin even when the relevant potential is singular at…
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 Comment by Duval et al. [PRL 96, 099701 (2006)] addresses an important, but not the main, result of our Letter [PRL 95, 137204 (2005)]. It does not contradict our results in substance, and the only objection is really on the style of…
In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable…
We make some comments about the results we obtained in Phys. Rev. Lett. 86,3392(2001), and in Phys. Rev. Lett.87, 177206 (2001), and show that the conclusion of a recent paper [cond-mat/0409495] leveling some criticism on our results is, in…
We show that the analysis presented in a recent comment by Coll and Ferrando \cite{comment} (qr-qc/0312058) is based on the erroneous assumption that the chemical potential and fractional concentration of a {\it mixture} of perfect fluids…
In a recent Comment [arXiv: 1101.3980] Shalaby criticised our paper "Families of Particles with Different Masses in PT-Symmetric Quantum Field Theory" [arXiv:1002.3253]. On examining his arguments, we find that there are serious flaws at…
We present a new set of infinitely many shape invariant potentials and the corresponding exceptional (X_{\ell}) Laguerre polynomials. They are to supplement the recently derived two sets of infinitely many shape invariant thus exactly…
We derive the leading quantum corrections to the gravitational potentials in a de Sitter background, due to the vacuum polarization from loops of conformal fields. Our results are valid for arbitrary conformal theories, even strongly…
We give conditions for $f$-positivity of relative complete intersections in projective bundles. We also derive an instability result for the fibres.
In a Comment [Phys. Rev. Lett. 113, 029801 (2014)] on our Letter on self-propelled asymmetric particles [Phys. Rev. Lett. 110, 198302 (2013); arXiv:1302.5787], Felderhof claims that our theory based on Langevin equations would be…
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…