Related papers: WKB Approximation with Conformable Operator
A method, recently devised to obtain analytical approximations to certain classes of integrals, is used in combination with the WKB expansion to derive accurate analytical expressions for the spectrum of quantum potentials. The accuracy of…
A set of simple exactly solvable potentials are shown to have convergent WKB series. The resulting all-orders quantisation conditions provide a unified description of all known cases where an exact WKB quantisation condition has been…
In the present work the conditions appearing in the WKB approximation formalism of quantum mechanics are analyzed. It is shown that, in general, a careful definition of an approximation method requires the introduction of two length…
This article is devoted to the construction of pseudomodes of one-dimensional biharmonic operators with the complex-valued potentials via the WKB method. As a by-product, the shape of pseudospectrum near infinity can be described. This is a…
The SWKB quantization condition is an exact quantization condition for the conventional shape-invariant potentials. On the other hand, this condition equation does not hold for other known solvable systems. The origin of the (non-)exactness…
We explore the possibility of modifying the Lewis-Riesenfeld method of invariants developed originally to find exact solutions for time-dependent quantum mechanical systems for the situation in which an exact invariant can be constructed,…
A conformable time-scale fractional calculus of order $\alpha \in ]0,1]$ is introduced. The basic tools for fractional differentiation and fractional integration are then developed. The Hilger time-scale calculus is obtained as a particular…
In this paper we develop an analogue of Hamilton-Jacobi theory for the time-evolution operator of a quantum many-particle system. The theory offers a useful approach to develop approximations to the time-evolution operator, and also…
In a previous paper it was shown that a one-turning-point WKB approximation gives an accurate picture of the spectrum of certain non-Hermitian PT-symmetric Hamiltonians on a finite interval with Dirichlet boundary conditions. Potentials to…
We approximate given potentials by means of the specially introduced reference potentials. On the one hand their parameters may be easily found from the usual WKB integral for the given potential; on the other hand they allow a simple…
Taking into account results of WKB-approximation, we derive exact quantum energies and wave functions of even and odd states in the one-dimensional Coulomb potential
Following the verification of the conjecture made by Comtet, Bandrauk and Campbell that the supersymmetry-inspired semiclassical method known as SWKB is exact for the conventional additive shape invariant potentials, it was widely believed…
We show that the approximation numbers of a compact composition operator on the weighted Bergman spaces $\mathfrak{B}_\alpha$ of the unit disk can tend to 0 arbitrarily slowly, but that they never tend quickly to 0: they grow at least…
The simple, longitudinal, and transverse wobblers are systematically studied within the framework of collective Hamiltonian, where the collective potential and mass parameter included are obtained based on the tilted axis cranking approach.…
The WKB approximation plays an essential role in the development of quantum mechanics and various important results have been obtained from it. In this paper, we introduce another method, {\it the so-called uniform asymptotic…
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 discuss the numerical solution of initial value problems for $\varepsilon^2\,\varphi''+a(x)\,\varphi=0$ in the highly oscillatory regime, i.e., with $a(x)>0$ and $0<\varepsilon\ll 1$. We analyze and implement an approximate solution…
We study the numerical approximation of fractional powers of accretive operators in this paper. Namely, if $A$ is the accretive operator associated with an accretive sesquilinear form $A(\cdot,\cdot)$ defined on a Hilbert space $\mathbb V$…
The exactness of the semiclassical method for three-dimensional problems in quantum mechanics is analyzed. The wave equation appropriate in the quasiclassical region is derived. It is shown that application of the standard leading-order WKB…
By means of numerical solutions of the quantum Hamilton Jacobi equation, a general WKB-like representation for one-dimensional wave functions is obtained. This representation is unique in the classically forbidden regions, while in the…