Interaction potential matrix elements for single-particle scattering off a simple harmonic oscillator

1996 ◽  
Vol 111 (5) ◽  
pp. 549-560
Author(s):  
P. L. Nash
Keyword(s):  
Harmonic Oscillator ◽  
Interaction Potential ◽  
Single Particle ◽  
Particle Scattering ◽  
Matrix Elements ◽  
Simple Harmonic Oscillator ◽  
Potential Matrix

Quantum algebras and parity-dependent spectra

2007 ◽  
Vol 463 (2086) ◽  
pp. 2415-2427 ◽  
Author(s):  
C.V Sukumar ◽  
Andrew Hodges
Keyword(s):  
Quantum Optics ◽  
Harmonic Oscillator ◽  
Combinatorial Theory ◽  
Squeezed States ◽  
Quantum Algebras ◽  
Matrix Elements ◽  
Euler Numbers ◽  
Simple Harmonic Oscillator ◽  
Non Gaussian ◽  
Special Case

We study the structure of a quantum algebra in which a parity-violating term modifies the standard commutation relation between the creation and annihilation operators of the simple harmonic oscillator. We discuss several useful applications of the modified algebra. We show that the Bernoulli and Euler numbers arise naturally in a special case. We also show a connection with Gaussian and non-Gaussian squeezed states of the simple harmonic oscillator. Such states have been considered in quantum optics. The combinatorial theory of Bernoulli and Euler numbers is developed and used to calculate matrix elements for squeezed states.

Brueckner Self-Consistent Study of 16O and 40Ca Using Phase-Shift Determined Potentials

1973 ◽  
Vol 51 (2) ◽  
pp. 115-120 ◽  
Author(s):  
R. J. W. Hodgson ◽  
Tran Duc Hoang
Keyword(s):  
Binding Energy ◽  
Phase Shift ◽  
Harmonic Oscillator ◽  
Single Particle ◽  
Effective Interaction ◽  
Scattering Data ◽  
Matrix Elements ◽  
High Energies ◽  
Self Consistent

A self-consistent Brueckner calculation of the binding energy and single-particle energies of 16O and 40Ca is carried out employing an effective interaction which is determined directly from the two-body scattering data. The interaction is described by its harmonic-oscillator matrix elements. It is found that the results are quite sensitive to the form of the phase shift at high energies.

scholarly journals Analytical angular solutions for the atom–diatom interaction potential in a basis set of products of two spherical harmonics: two approaches

2021 ◽  
Author(s):  
Mariusz Pawlak ◽  
Marcin Stachowiak
Keyword(s):  
Spherical Harmonics ◽  
Interaction Potential ◽  
Chem Phys ◽  
Basis Set ◽  
Matrix Elements ◽  
Trigonometric Functions ◽  
Variational Theory ◽  
Molecular Collision ◽  
The Matrix ◽  
Analytical Expressions

AbstractWe present general analytical expressions for the matrix elements of the atom–diatom interaction potential, expanded in terms of Legendre polynomials, in a basis set of products of two spherical harmonics, especially significant to the recently developed adiabatic variational theory for cold molecular collision experiments [J. Chem. Phys. 143, 074114 (2015); J. Phys. Chem. A 121, 2194 (2017)]. We used two approaches in our studies. The first involves the evaluation of the integral containing trigonometric functions with arbitrary powers. The second approach is based on the theorem of addition of spherical harmonics.

Harmonic Oscillators with Nonlinear Damping

2017 ◽  
Vol 27 (11) ◽  
pp. 1730037 ◽  
Author(s):  
J. C. Sprott ◽  
W. G. Hoover
Keyword(s):  
Dynamical Systems ◽  
Harmonic Oscillator ◽  
Strange Attractor ◽  
Nonlinear Damping ◽  
Harmonic Oscillators ◽  
Coexisting Attractors ◽  
Simple Harmonic Oscillator ◽  
Interesting Behavior

Dynamical systems with special properties are continually being proposed and studied. Many of these systems are variants of the simple harmonic oscillator with nonlinear damping. This paper characterizes these systems as a hierarchy of increasingly complicated equations with correspondingly interesting behavior, including coexisting attractors, chaos in the absence of equilibria, and strange attractor/repellor pairs.

Propagator for the simple harmonic oscillator

1998 ◽  
Vol 66 (11) ◽  
pp. 1022-1024 ◽  
Author(s):  
Nora S. Thornber ◽  
Edwin F. Taylor
Keyword(s):  
Harmonic Oscillator ◽  
Simple Harmonic Oscillator

Single-particle scattering effects on the resonance modes of microdroplets

1997 ◽  
Vol 36 (33) ◽  
pp. 8521
Author(s):  
Hee-Jong Moon ◽  
Guang-Hoon Kim ◽  
Kwang-Hoon Ko ◽  
Jai-Hyung Lee ◽  
Joon-Sung Chang
Keyword(s):  
Single Particle ◽  
Particle Scattering ◽  
Resonance Modes ◽  
Scattering Effects
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