Shape invariant potential formalism for photon-added coherent state construction

An algebro-operator approach, called shape invariant potential method, of constructing generalized coherent states for photon-added particle system is presented. Illustration is given on Poschl-Teller potential

On Hilbert-Schmidt operator formulation of noncommutative quantum mechanics

This work gives value to the importance of Hilbert-Schmidt operators in the formulation of a noncommutative quantum theory. A system of charged particle in a constant magnetic field is investigated in this framework

All-particle Hamiltonians for Polyatomic-molecules .1. Body-fixed Frames and Coordinates - Classical Treatment

With a view to quantization, exact classical expressions of Hamiltonians are derived for a molecular system made up of nu-electrons and N nuclei, by applying a body-fixed (BF) matrix procedure recently introduced. Two cases are considered, depending on whether the BF frame origin is at the centre of mass of the nuclei or at the total centre of mass. The arrangement of the nuclei is described by 3N - 6 internal coordinates, and the 3-nu-electron BF Cartesian coordinates are used. All terms which contribute to the total energy are identified. The similarities and the differences between the two cases are emphasized, particularly with regard to the consequences of (i) neglecting the electron/total system mass ratio, (ii) the assumption of infinitely slow nuclear motion and the fact that (iii) there can be either no distinction between the body-fixed and the space-fixed frames, i.e. no overall rotation, or not, i.e. no total angular momentum is considered. The separability of the Hamiltonians is discussed

New families of orthogonal polynomials

This paper provides with a generalization of the work by Wimp and Kiesel [Non-linear recurrence relations and some derived orthogonal polynomials, Ann. Numer. Math. 2 (1995) 169-180] who generated some new orthogonal polynomials from Chebyshev polynomials of second kind. We consider a class of polynomials P-n(x) defined by: P-n(x) = (a(n)x + b(n)) Pn-1(x) + (1 - a(n)) P-n (x), n = 0, 1, 2,..., a(0) not equal 1, where the P-k(x) are monic classical orthogonal polynomials satisfying the well-known three-term recurrence relation: Pn+1(x) = (x - beta(n))P-n(x) - gamma P-n(n-1)(x), n >= 1, P-1(x) = x - beta(0); P-0 (x) = 1. We explicitly derive the sequences a(n) and b(n) in general and illustrate by some concrete relevant examples. (c) 2005 Elsevier B.V. All rights reserved

All-particle Hamiltonians for Polyatomic-molecules .2. Born-oppenheimer and Other Adiabatic Approximations

A non-relativistic exact quantum-mechanical expression of the Hamiltonian operator is derived for a molecular system made up of nu-electrons and N nuclei, by following a body-fixed quantization procedure recently introduced. The BF frame origin is at the total centre of mass. The arrangement of the nuclei is described by 3N - 6 internal coordinates, and the 3-nu-electron body-fixed Cartesian coordinates are used. All terms that contribute, beyond the Born-Oppenheimer electronic Hamiltonian, to the non-adiabatic couplings are identified. The difference between the Born-Oppenheimer approximation (based on the infinitely slow nuclear motion hypothesis and no distinction between the body-fixed and space-fixed frames, i.e. no overall rotation), and the adiabatic approximations based on the infinitely slow nuclear motion hypothesis and no total or nuclear angular momentum, is emphasized. The separability of the total Hamiltonian operator is discussed