Related papers: Exceptional orthogonal polynomials, QHJ formalism …
Higher-order WKB methods are used to investigate the border between the solvable and insolvable portions of the spectrum of quasi-exactly solvable quantum-mechanical potentials. The analysis reveals scaling and factorization properties that…
Two sets of infinitely many exceptional orthogonal polynomials related to the Wilson and Askey-Wilson polynomials are presented. They are derived as the eigenfunctions of shape invariant and thus exactly solvable quantum mechanical…
We explore the exact-WKB (EWKB) method through the analysis of Airy and Weber types, with an emphasis on the exact quantization of locally harmonic potentials in multiple sectors. The core innovation of our work lies in introducing a novel…
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…
Classical mechanics admits multiple equivalent formulations, from Newton's equations to the variational Lagrange-Hamilton framework and the scalar Hamilton-Jacobi (HJ) theory. In the HJ formulation, classical ensembles evolve through the…
A comprehensive review of exactly solvable quantum mechanics is presented with the emphasis of the recently discovered multi-indexed orthogonal polynomials. The main subjects to be discussed are the factorised Hamiltonians, the general…
The multi-indexed Jacobi polynomials are the main part of the eigenfunctions of exactly solvable quantum mechanical systems obtained by certain deformations of the P\"oschl-Teller potential (Odake-Sasaki). By fine-tuning the parameter(s) of…
In this paper, we sketch and emphasize the automatic emergence of a quantum potential (QP) in general Hamilton-Jacobi equation via commuting relations, quantum canonical transformations and without the straight effect of wave function. The…
We apply a simple transformation method to construct a set of new exactly solvable potentials (ESP) which gives rise to bound state solution of $D$-dimensional Schr\"odinger equation. The important property of such exactly solvable quantum…
Certain aspects of the integrability/solvability of the Calogero-Sutherland-Moser systems and the Ruijsenaars-Schneider-van Diejen systems with rational and trigonometric potentials are reviewed. The equilibrium positions of classical…
In this paper we solve the eigenvalue problem of the angular momentum operator by using the supersymmetric semiclassical quantum mechanics (SWKB), and show that it gives the correct quantization already at the leading order.
In this paper, the theory of the fractional singular Lagrangian systems is investigated with second order derivatives. The fractional quantization for these systems is examined using the WKB approximation. The Hamilton Jacobi treatment can…
This paper is devoted to studying the Hamilton-Jacobi-Bellman equations with distribution-valued coefficients, which is not well-defined in the classical sense and shall be understood by using paracontrolled distribution method introduced…
The Quantum Stationary HJ Equation (QSHJE) that we derived from the equivalence principle, gives rise to initial conditions which cannot be seen in the Schroedinger equation. Existence of the classical limit leads to a dependence of the…
By exploiting the hidden algebraic structure of the Schrodinger Hamiltonian, namely the sl(2), we propose a unified approach of generating both exactly solvable and quasi-exactly solvable quantum potentials. We obtain, in this way, two new…
The Hamiltonian treatment of constrained systems in $G\ddot{u}ler's$ formalism leads us to the total differential equations in many variables. These equations are integrable if the corresponding system of partial differential equations is a…
We derive the analytical eigenvalues and eigenstates of a family of potentials wells with exponential form (FPWEF). We provide a brief summary of the supersymmetry formalism applied to quantum mechanics and illustrate it by producing from…
It has been shown that the cases of the JWKB formulae in 1--dim QM quantizing the energy levels exactly are results of essentially one global symmetry of both potentials and their corresponding Stokes graphs. Namely, this is the invariance…
We apply the H-FGK formalism to the study of some properties of the general class of black holes in N=2 supergravity in four dimensions that correspond to the harmonic and hyperbolic ansatze and obtain explicit extremal and non-extremal…
Eigenstates of the FQHE hamiltonian problem after to be projected on the LLL are determined for filling factors 1/q, with q an odd number. The solutions are found for an infinite class of finite samples in which the Coulomb potential is…