相关论文: A new coherent states approach to semiclassics whi…

We introduce new coherent states and use them to prove semi-classical estimates for Schr\"odinger operators with regular potentials. This can be further applied to the Thomas-Fermi potential yielding a new proof of the Scott correction for…

We prove the first correction to the leading Thomas-Fermi energy for the ground state energy of atoms and molecules in a model where the kinetic energy of the electrons is treated relativistically. The leading Thomas-Fermi energy,…

In a recent short note [Bergeron H, Gazeau J P, Siegl P and Youssef A 2010 EPL 92 60003], we have presented the nice properties of a new family of semi-classical states for P\"oschl-Teller potentials. These states are built from a…

We present a construction of semi-classical states for P\"oschl-Teller potentials based on a supersymmetric quantum mechanics approach. The parameters of these "coherent" states are points in the classical phase space of these systems. They…

We present a novel analytical method for calculating the spectral function and the density of states in speckle potentials, valid in the semiclassical regime. Our approach relies on stationary phase approximations, allowing us to describe…

The concept of near resonances for harmonic approximations of semiclassical Schr\"odinger operators is introduced and explored. Combined with a natural extension of the Birkhoff-Gustavson normal form, we obtain formulas for approaching the…

We propose a new analytical method to solve for the nonexactly solvable Schrodinger equation. Successfully, it is applied to a class of spiked harmonic oscillators and truncated Coulomb potentials. The utility of this method could be…

We have discovered a class of dynamically stable coherent states for motion on the half-line. The regularization of the half-line boundary and the consequent quantum motion are expounded within the framework of covariant affine…

We consider relativistic many-particle operators which - according to Brown and Ravenhall - describe the electronic states of heavy atoms. Their ground state energy is investigated in the limit of large nuclear charge and velocity of light.…

By using the overcompleteness of coherent states we find an alternative form of the unit operator for which the ket and the bra appearing under the integration sign do not refer to the same phase-space point. This defines a new quantum…

A certain modification of the semiclassical quantization condition based on the summarization of the known power expansion in the squared Planck constant is proposed. Corresponding deviation from exact spectra arises only together with the…

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 method of integrals of motion is used to construct families of generalized coherent states of a nonrelativistic spinless charged particle in a constant electric field. Families of states, differing in the values of their standard…

We demonstrate how a certain new form of the quantization condition proposed earlier can be used outside the class of potentials for which this form ensures exact spectra. Taking this form as a base we get an improved interpolating…

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…

We apply a quantum version of dimensional reduction to Gaussian coherent states in Bargmann space to obtain squeezed states on complex projective spaces. This leads to a definition of a family of squeezed spin states with excellent…

We derive semiclassical quantization conditions for systems with spin. To this end one has to define the notion of integrability for the corresponding classical system which is given by a combination of the translational motion and…

In this paper, we propose an algorithm to construct coherent states for an exactly solvable position dependent mass Schr\"odinger equation. We use point canonical transformation method and obtain ground state eigenfunction of the position…

The notion of semi-classical states is first sharpened by clarifying two issues that appear to have been overlooked in the literature. Systems with linear and quadratic constraints are then considered and the group averaging procedure is…

As basic elements of the quantum computer - quantum bits (qubits) we offer semiconductor quantum dots containing one electron each and consisting each of two tunnel-connected parts. The numerical solution of a Schroedinger equation with the…