Related papers: Exactness of SWKB for Shape Invariant Potentials
We demonstrate how the Exact WKB analysis works in the study of the quasi-normal modes (QNMs). We apply the Exact WKB analysis to a massless scalar perturbation to the D3-brane metric as a concrete example. The Exact WKB analysis provides…
Superintegrable systems are classical and quantum Hamiltonian systems which enjoy much symmetry and structure that permit their solubility via analytic and even, algebraic means. They include such well-known and important models as the…
Maximally Natural Supersymmetry, an unusual weak-scale supersymmetric extension of the Standard Model based upon the inherently higher-dimensional mechanism of Scherk-Schwarz supersymmetry breaking (SSSB), possesses remarkably good fine…
A new form to construct complex superpotentials that produce real energy spectra in supersymmetric quantum mechanics is presented. This is based on the relation between the nonlinear Ermakov equation and a second order differential equation…
In this paper, we discuss the generalizations of exact supersymmetries present in the supersymmetrized sigma models. These generalizations are made by making the supersymmetric transformation parameter field-dependent. Remarkably, the…
One construction of exactly-solvable potentials for Fokker-Planck equation is considered based on supersymmetric quantum mechanics approach.
We review an exact analytical resolution method for general one-dimensional (1D) quantal anharmonic oscillators: stationary Schr\"odinger equations with polynomial potentials. It is an exact form of WKB treatment involving spectral (usual)…
A path-integral approach is used to study the spectral properties of the generators of the SO(2,1) symmetry of conformal quantum mechanics (CQM). In particular, we consider the CQM version that corresponds to the weak-coupling regime of the…
We present a simple derivation of the WKB quantisation condition using the quantum Hamilton-Jacobi formalism and propose an exact quantisation condition within this formalism for integrable models in higher dimensions.
We state and prove here semiclassical results about the construction of asymptotic solutions by the WKB method for pseudo-differential equations of real principal type. It is a Gevrey version; the smooth $C^\infty$ and the analytic ones may…
The J-matrix method of scattering was developed to handle regular short-range potentials with applications in atomic, nuclear and molecular physics. Its accuracy, stability, and convergence properties compare favorably with other successful…
We consider Witten Laplacians associated to some non-Morse potentials. We prove Eyring-Kramers formulas for the bottom of the spectrum of these operators in the semiclassical regime and quantify the spectral gap separating these eigenvalues…
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…
A quantization procedure, which has recently been introduced for the analysis of Painlev\'e equations, is applied to a general time-independent potential of a Newton equation. This analysis shows that the quantization procedure preserves…
Resonance phenomena are central to many quantum systems, where resonant states are typically characterized by pole singularities of the S-matrix. In this work, we employ the complex scaling method (CSM) in conjunction with exact WKB…
We investigate the massless scalar quasinormal modes (QNMs) of the noncommutative $D$-dimensional Schwarzschild-Tangherlini black hole spacetime in this paper. By using the Wentzel-Kramers-Brillouin (WKB) approximation method, the…
Spin-weighted spheroidal harmonics play a central role in the mathematical description of diverse physical phenomena, including black-hole perturbation theory and wave scattering. We present a novel and compact derivation of the asymptotic…
We report a new shape invariant (SI) isospectral extension of the Morse potential. Previous investigations have shown that the list of "conventional" SI superpotentials that do not depend explicitly on Planck's constant $\hbar$ is complete.…
Two-dimensional Scarf~II quantum model is considered in the framework of Supersymmetrical Quantum Mechanics (SUSY QM). Previously obtained results for this integrable system are systematized, and some new properties are derived. In…
We describe the space of (all) invariant deformation quantizations on the hyperbolic plane as solutions of the evolution of a second order hyperbolic differential operator. The construction is entirely explicit and relies on non-commutative…