Related papers: Semiclassical Expansion for the Angular Momentum
We look at the long-time behaviour of solutions to a semi-classical Schr\"odinger equation on the torus. We consider time scales which go to infinity when the semi-classical parameter goes to zero and we associate with each time-scale the…
An $\hbar$-expansion is presented for the ensemble-averaged spectral function of noninteracting matter waves in random potentials. We obtain the leading quantum corrections to the deep classical limit at high energies by the Wigner-Weyl…
We derive simple practical procedures revealing the quantum behavior of angular momentum variables by the violation of classical upper bounds on the statistics. Data analysis is minimum and definite conclusions are obtained without…
Bohr-Sommerfeld type quantization conditions of semiclassical eigenvalues for the non-selfadjoint Zakharov-Shabat operator on the circle are derived using an exact WKB method. The conditions are given in terms of the action associated with…
Invoking Maxwell's classical equations in conjunction with expressions for the electromagnetic (EM) energy, momentum, force, and torque, we use a few simple examples to demonstrate the nature of the EM angular momentum. The energy and the…
For two Coulombically interacting electrons in a quantum dot with harmonic confinement and a constant magnetic field, we show that time-dependent semiclassical calculations using the Herman-Kluk initial value representation of the…
We study the coupled system of Maxwell and Dirac equations from a semiclassical point of view. A rigorous nonlinear WKB-analysis, locally in time, for solutions of (critical) order $O(\sqrt{\epsilon})$ is performed, where the small…
We present a novel deep learning method for computing eigenvalues of the fractional Schr\"odinger operator. Our approach combines a newly developed loss function with an innovative neural network architecture that incorporates prior…
We derive semiclassical periodic orbit expansions for a correlation function of the Wigner time delay. We consider the Fourier transform of the two-point correlation function, the form factor $K(\tau,x,y,M)$, that depends on the number of…
We give a survey of some results, mainly obtained by the authors and their collaborators, on spectral properties of the magnetic Schr\"odinger operators in the semiclassical limit. We focus our discussion on asymptotic behavior of the…
We derive the semiclassical WKB quantization condition for obtaining the energy band edges of periodic potentials. The derivation is based on an approach which is much simpler than the usual method of interpolating with linear potentials in…
We have developed a semiclassical approach to solving the Bogoliubov - de Gennes equations for superconductors. It is based on the study of classical orbits governed by an effective Hamiltonian corresponding to the quasiparticles in the…
We first prove semiclassical resolvent estimates for the Schr{\"o}dinger operator in R d , d $\ge$ 3, with real-valued potentials which are H{\"o}lder with respect to the radial variable. Then we extend these resolvent estimates to exterior…
We propose a discussion of angular momentum and its Euler equation, with the aim of giving a short outline of their history. This outline can be useful for teaching purposes too, to amend some problems that students can have in learning…
Several techniques for deriving semianalytical bounds on the energy eigenvalues of the spinless Salpeter equation and for estimating the quality of the corresponding approximate eigenstates are reviewed.
An exact semiclassical version of the classical KAM theorem about small perturbations of vector fields on the torus is given. Moreover, a renormalization theorem based on counterterms for some semiclassical systems that are close to being…
We describe the behaviour of semiclassical electrodynamics under gauge transformations. For this purpose we observe the structure of Schr\"odinger equation and matricial elements under these transformations. We conclude this theory is not…
We study the dynamics of a quantum particle in R^(n+m) constrained by a strong potential force to stay within a distance of order hbar (in suitable units) from a smooth n-dimensional submanifold M. We prove that in the semiclassical limit…
The Bertrand's theorem is extended, i.e. closed orbits still may exist for other central potentials than the power law Coulomb potential and isotropic harmonic oscillator. It is shown that for the combined potential $V(r)=W(r)+b/r^2$…
In this paper, we study the semiclassical limit for the stationary magnetic nonlinear Schr\"odinger equation \begin{align}\label{eq:initialabstract}\left( i \hbar \nabla + A(x) \right)^2 u + V(x) u = |u|^{p-2} u, \quad x\in…