Analytical expressions and recursion relations of two-center harmonic oscillator matrix elements of arbitrary functions

1990 ◽  
Vol 37 (6) ◽  
pp. 797-809 ◽  
Author(s):  
P. J. Drallos ◽  
J. M. Wadehra
Keyword(s):  
Harmonic Oscillator ◽  
Matrix Elements ◽  
Recursion Relations ◽  
Analytical Expressions

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.

Matrix elements of the radial-angular factorized harmonic oscillator

1972 ◽  
Vol 12 (2) ◽  
pp. 185-196 ◽  
Author(s):  
T. G. Haskell ◽  
B. G. Wyboturne
Keyword(s):  
Harmonic Oscillator ◽  
Matrix Elements

Comparative analysis of properties for amplified coherent state and amplified squeezed vacuum

2020 ◽  
Vol 34 (33) ◽  
pp. 2050377
Author(s):  
Yan-Bei Cheng ◽  
Sheng-Guo Guan ◽  
Zu-Jian Wang ◽  
Xue-Xiang Xu
Keyword(s):  
Comparative Analysis ◽  
Coherent State ◽  
Amplification Factor ◽  
Annihilation Operator ◽  
Photon Number ◽  
Matrix Elements ◽  
Squeezed Vacuum ◽  
Quadrature Squeezing ◽  
Antibunching Effect ◽  
Analytical Expressions

Two “amplified” quantum states, that is, amplified coherent state (ACS) and amplified squeezed vacuum (ASV), are considered in this paper by applying operator [Formula: see text] on coherent state (CS) and squeezed vacuum (SV), respectively. Here [Formula: see text] [Formula: see text] denotes a amplification factor and [Formula: see text]) denote the creation (annihilation) operator. Along these two lines, we make a comparative analysis of properties for ACS and ASV. The considered properties include density matrix elements, Wigner function, mean photon number, second-order autocorrelation function, and quadrature squeezing. We derive analytical expressions and make numerical simulations for all the properties. The noteworthy results include: (1) the ACS has antibunching and squeezing characters; (2) the ASV will have the bunching and antibunching effect in small initial squeezing.

Matrix Elements of the Lorentzian Term

1976 ◽  
Vol 31 (6) ◽  
pp. 553-556 ◽  
Author(s):  
Ch. V. S. Ramachandrá Rao
Keyword(s):  
Harmonic Oscillator ◽  
Matrix Elements ◽  
Practical Application ◽  
The Matrix

Recursion formulae for the matrix elements of the Lorentzian term 1/(C2 + q2) as well as 1/(C2 + q2)2, on the basis of harmonic oscillator eigenfunctions, are obtained. A practical application where these formulae would be useful is discussed

Approach of the continuous q-Hermite polynomials to x-representation of q-oscillator algebra and its coherent states

2019 ◽  
Vol 17 (02) ◽  
pp. 2050021
Author(s):  
H. Fakhri ◽  
S. E. Mousavi Gharalari
Keyword(s):  
Harmonic Oscillator ◽  
Generating Function ◽  
Coherent States ◽  
Finite Interval ◽  
Hermite Polynomials ◽  
Oscillator Algebra ◽  
Text Representation ◽  
Ladder Operators ◽  
Recursion Relations ◽  
Wilson Operator

We use the recursion relations of the continuous [Formula: see text]-Hermite polynomials and obtain the [Formula: see text]-difference realizations of the ladder operators of a [Formula: see text]-oscillator algebra in terms of the Askey–Wilson operator. For [Formula: see text]-deformed coherent states associated with a disc in the radius [Formula: see text], we obtain a compact form in [Formula: see text]-representation by using the generating function of the continuous [Formula: see text]-Hermite polynomials, too. In this way, we obtain a [Formula: see text]-difference realization for the [Formula: see text]-oscillator algebra in the finite interval [Formula: see text] as a [Formula: see text]-generalization of known differential formalism with respect to [Formula: see text] in the interval [Formula: see text] of the simple harmonic oscillator.

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