Related papers: SWKB Quantization Condition for Conditionally Exac…
We analyze quantitatively the accuracy of eigenfunction and eigenvalue calculations in the frame work of WKB and instanton semiclassical methods. We show that to estimate the accuracy it is enough to compare two linearly independent (with…
Following earlier studies, several new features of singular perturbation theory for one-dimensional quantum anharmonic oscillators are computed by exact WKB analysis; former results are thus validated.
Version 1: The well known Eckart's singular s-wave potential is PT-symmetrically regularized and continued to the whole real line. The new model remains exactly solvable and its bound states remain proportional to Jacobi polynomials. Its…
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 uncover an inconsistency in the uniform WKB quantization of deformed quantum mechanics.
Certain quantum mechanical systems with a discrete spectrum, whose observables are given by a transseries in $\hbar$, were shown to admit $\hbar_0$-deformations with Borel resummable expansions which reproduce the original model at…
We consider exact WKB analysis to a ${\cal PT}$ symmetric quantum mechanics defined by the potential, $V(x) = \omega^2 x^2 + g x^2(i x)^{\varepsilon=2}$ with $\omega \in {\mathbb R}_{\ge 0}$, $g \in {\mathbb R} _{> 0}$. We in particular aim…
Coherent feedback control considers purely quantum controllers in order to overcome disadvantages such as the acquisition of suitable quantum information, quantum error correction, etc. These approaches lack a systematic characterization of…
The entanglement of formation gives a necessary and sufficient condition for the existence of a perfect quantum error correction procedure.
Semiclassical methods are essential in analyzing quantum mechanical systems. Although they generally produce approximate results, relatively rare potentials exist for which these methods are exact. Such intriguing potentials serve as…
The paper deals with Hawking radiation related to non-static spherically symmetric black hole. Quantum corrections are incorporated using Hamilton-Jacobi method beyond semi-classical approximation. It is found that different order…
The Hamilton-Jacobi method of constrained systems is discussed. The equations of motion for three singular systems are obtained as total differential equations in many variables. The integrability conditions for these syatems lead us to the…
In this article we discuss which controllability properties of classical Hamiltonian systems are preserved after quantization. We discuss some necessary and some sufficient conditions for small-time controllability of classical systems and…
A supersymmetric method for the construction of so-called conditionally exactly solvable quantum systems is reviewed and extended to classical stochastic dynamical systems characterized by a Fokker-Planck equation with drift. A class of…
We make use of the Quantum Hamilton-Jacobi (QHJ) theory to investigate conditional quasi-solvability of the quantum symmetric top subject to combined electric fields (symmetric top pendulum). We derive the conditions of quasi-solvability of…
An arbitrary renormalizable quantum field theory is considered as finite if its dimensionless couplings conspire to yield, at every order of its perturbative expansion, no ultraviolet-divergent renormalizations of the physical parameters of…
We discuss the Hamilton-Jacobi approach for a constrained system. We obtain the equation of motion for a singular system as total differential equations in many variables. We investigate the integrability conditions without using any gauge…
Gauge invariance of systems whose Hamilton-Jacobi equation is separable is improved by adding surface terms to the action fuctional. The general form of these terms is given for some complete solutions of the Hamilton-Jacobi equation. The…
General analytical solutions of the Quantum Hamilton Jacobi Equation for conservative one-dimensional or reducible motion are presented and discussed. The quantum Hamilton's characteristic function and its derivative, i.e. the quantum…
We investigate exact semidefinite programming (SDP) relaxations for the problem of minimizing a nonconvex quadratic objective function over a feasible region defined by both finitely and infinitely many nonconvex quadratic inequality…