Related papers: SWKB and proper quantization conditions for transl…
The formalism of Supersymmetric Quantum Mechanics supplies a trial wave function to be used in the Variational Method. The screened Coulomb potential is analysed within this approach. Numerical and exact results for energy eigenvalues are…
This paper identifies a new class of shape invariant models. These models are based on extensions of conventional quantum mechanics that satisfy a string-motivated minimal length uncertainty relation. An important feature of our…
A simple and algorithmic description of matrix shape invariant potentials is presented. The complete lists of generic matrix superpotentials of dimension $2\times2$ and of special superpotentials of dimension $3\times3$ are given…
We comment that the conditionally exactly solvable potential of Dutt et al. and the exactly solvable potential from which it is derived form a dual system.
Solutions obtained by the quasilinearization method (QLM) are compared with the WKB solutions. Expansion of the $p$-th QLM iterate in powers of $\hbar$ reproduces the structure of the WKB series generating an infinite number of the WKB…
The equivalence postulate of quantum mechanics offers an axiomatic approach to quantum field theories and quantum gravity. The equivalence hypothesis can be viewed as adaptation of the classical Hamilton-Jacobi formalism to quantum…
We present a new family of shape invariant potentials which could be called a ``continuous \ell version" of the potentials corresponding to the exceptional (X_{\ell}) J1 Jacobi polynomials constructed recently by the present authors. In a…
We investigate the exact-WKB analysis for quantum mechanics in a periodic potential, with $N $ minima on $S^{1}$. We describe the Stokes graphs of a general potential problem as a network of Airy-type or degenerate Weber-type building…
All simple translation-invariant valuations on polytopes are classified. As a direct consequence the well-known conditions for translative-equidecomposability are recovered. Furthermore, a simplified proof of the classification of…
An algebraic treatment of shape-invariant potentials is discussed. By introducing an operator which reparametrizes wavefunctions, the shape-invariance condition can be related to a generalized Heisenberg- Weyl algebra. It is shown that this…
We propose a new variant of the semiclassical quantisation with two independent parameters. The first one is proportional to the Planck constant as usually and the second one is connected with a deviation of the given potential from a very…
We give two conditionally exactly solvable inverse power law potentials whose linearly independent solutions include a sum of two confluent hypergeometric functions. We notice that they are partner potentials and multiplicative shape…
We have obtained the general form of even mode potential function for the gravitational perturbation of a static spherically symmetric spacetime. Considering the minimal-spread Gaussian matter source, parameterized by a smearing length…
We present an explicit expression for the topological invariants associated to $SU(2)$ monopoles in the fundamental representation on spin four-manifolds. The computation of these invariants is based on the analysis of their corresponding…
We propose a new method for constructing the quasi-exactly solvable (QES) potentials with two known eigenstates using supersymmetric quantum mechanics. General expression for QES potentials with explicitly known energy levels and wave…
For supersymmetric gauge theories a consistent regularization scheme that preserves supersymmetry and gauge invariance is not known. In this article we tackle this problem for supersymmetric QED within the framework of algebraic…
It is shown that quantum mechanics on noncommutative spaces (NQM) can be obtained by the canonical quantization of some underlying second class constrained system formulated in extended configuration space. It leads, in particular, to an…
The Maslov index in the semiclassical Bohr-Sommerfeld quantization rule is calculated for one-dimensional power-law potentials. The result for the inverse square root potential is compared with the recently reported exact solution. The case…
Quantum resource theories provide a mathematically rigorous way of understanding the nature of various quantum resources. An important problem in any quantum resource theory is to determine how quantum states can be converted into each…
We report progress on extending the relativistic model-independent quantization condition for three particles, derived previously by two of us, to a broader class of theories, as well as progress on checking the formalism. In particular, we…