相关论文: Semiclassical Expansion for the Angular Momentum

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.

We calculate the WKB series for the angular momentum and the non--relativistic 3-dim Kepler problem. This is the first semiclassical treatment of the angular momentum for terms beyond the leading WKB approximation. We explain why the torus…

The aim of this paper is to provide uniform estimates for the eigenvalue spacings of one-dimensional semiclassical Schr\"odinger operators with singular potentials on the half-line. We introduce a new development of semiclassical measures…

The three-dimensional Schredinger's equation is analyzed with the help of the correspondence principle between classical and quantum-mechanical quantities. Separation is performed after reduction of the original equation to the form of the…

This paper is concerned with the efficient numerical computation of solutions to the 1D stationary Schr\"odinger equation in the semiclassical limit in the highly oscillatory regime. A previous approach to this problem based on explicitly…

A class of singular integral operators, encompassing two physically relevant cases arising in perturbative QCD and in classical fluid dynamics, is presented and analyzed. It is shown that three special values of the parameters allow for an…

A large time expansion for the propagator associated to a semiclassical non-selfadjoint magnetic Schr\"odinger operator is established, in terms of the low lying eigenvalues of the operator.

We review some results concerning the semi-classical limit for the nonlinear Schrodinger equation, with or without an external potential. We consider initial data which are either of the WKB type, or very concentrated as the semi-classical…

The explicit semiclassical treatment of logarithmic perturbation theory for the nonrelativistic bound states problem is developed. Based upon $\hbar$-expansions and suitable quantization conditions a new procedure for deriving perturbation…

In this article we study the semiclassical spectral measures associated with Schr\"odinger operators on $R^n$. In particular we compute the first few coefficients of the asymptotic expansions of these measures and, as an application, give…

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…

The Agmon estimate for multi-dimensional discrete Schr\"{o}dinger operators is studied with emphasis on the microlocal analysis on the torus. We first consider the semiclassical setting where semiclassical continuous Schr\"{o}dinger…

Analytical solutions of the Schrodinger equation are obtained for some diatomic molecular potentials with any angular momentum. The energy eigenvalues and wave functions are calculated exactly. The asymptotic form of the equation is also…

For the semi-classical limit of the cubic, defocusing nonlinear Schrodinger equation with an external potential, we explain the notion of criticality before a caustic is formed. In the sub-critical and critical cases, we justify the WKB…

We propose a way to study one-dimensional statistical mechanics models with complex-valued action using transfer operators. The argument consists of two steps. First, the contour of integration is deformed so that the associated transfer…

Based on the novel prescription for the power of a complex number, a new expression for the eigenfunction of the operator of the third component of the angular momentum is presented. These functions are normalizable, single valued and are…

A concept of semiclassically concentrated solutions is formulated for the multidimensional nonlinear Schr\"odinger equation (NLSE) with an external field. These solutions are considered as multidimensional solitary waves. The center of mass…

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…

We develop a modified semi-classical approach to the approximate solution of Schrodinger's equation for certain nonlinear quantum oscillations problems. At lowest order, the Hamilton-Jacobi equation of the conventional semi-classical…

The explicit semiclassical treatment of the logarithmic perturbation theory for the bound-state problem for the spherical anharmonic oscillator is developed. Based upon the $\hbar$-expansions and suitable quantization conditions a new…