The SU(2) realization for the Morse potential and its coherent states

2002 ◽  
Vol 80 (2) ◽  
pp. 129-139 ◽  
Author(s):  
S -H Dong
Keyword(s):  
Coherent States ◽  
Morse Potential ◽  
Transition Probability ◽  
Matrix Elements ◽  
Commutation Relations ◽  
Raising And Lowering Operators ◽  
The Matrix ◽  
Harmonic Perturbation ◽  
Analytical Expressions ◽  
Lowering Operators

A realization of the raising and lowering operators for the Morse potential is presented. We show that these operators satisfy the commutation relations for the SU(2) group. Closed analytical expressions are derived for the matrix elements of different functions such as 1/y and d/dy. The harmonic limit of the SU(2) operators is also studied. The transition probability between two eigenstates produced by a harmonic perturbation as a function of the operators [Formula: see text]±,0 is discussed. The average values of some observables in the coherent states |α > for the Morse potential are also calculated. PACS Nos.: 02.30+b, 03.65Fd, 42.50Ar, and 33.10Cs

ALGEBRAIC APPROACH TO THE PSEUDOHARMONIC OSCILLATOR IN 2D

2002 ◽  
Vol 11 (02) ◽  
pp. 155-160 ◽  
Author(s):  
SHI-HAI DONG ◽  
ZHONG-QI MA
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Algebraic Approach ◽  
Matrix Elements ◽  
Ladder Operators ◽  
Commutation Relations ◽  
The Matrix ◽  
Pseudoharmonic Oscillator ◽  
Analytical Expressions

A realization of the ladder operators for the solutions to the Schrödinger equation with a pseudoharmonic oscillator in 2D is presented. It is shown that those operators satisfy the commutation relations of an SU(1, 1) algebra. Closed analytical expressions are evaluated for the matrix elements of some operators r2 and r∂/∂ r

THE HIDDEN SYMMETRY FOR A QUANTUM SYSTEM WITH A PÖSCHL–TELLER-LIKE POTENTIAL

2003 ◽  
Vol 12 (06) ◽  
pp. 809-815 ◽  
Author(s):  
SHI-HAI DONG ◽  
GUO-HUA SUN ◽  
YU TANG
Keyword(s):  
Quantum System ◽  
Wave Functions ◽  
Matrix Elements ◽  
Eigenvalues And Eigenfunctions ◽  
Creation And Annihilation Operators ◽  
Commutation Relations ◽  
Hidden Symmetry ◽  
The Matrix ◽  
The Creation ◽  
Analytical Expressions

The eigenvalues and eigenfunctions of the Schrödinger equation with a Pöschl–Teller (PT)-like potential are presented. A realization of the creation and annihilation operators for the wave functions is carried out. It is shown that these operators satisfy the commutation relations of an SU(1,1) group. Closed analytical expressions are evaluated for the matrix elements of different functions, sin (ρ) and [Formula: see text] with ρ=πx/L.

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.

HAPPER'S CURIOUS DEGENERACIES AND YANGIAN

2002 ◽  
Vol 16 (14n15) ◽  
pp. 1867-1873 ◽  
Author(s):  
CHENG-MING BAI ◽  
MO-LIN GE ◽  
KANG XUE
Keyword(s):  
Representation Theory ◽  
Algebraic Structure ◽  
Zeeman Effect ◽  
Tensor Space ◽  
Commutation Relations ◽  
Raising And Lowering Operators ◽  
Degenerate States ◽  
Lowering Operators

We find raising and lowering operators distinguishing the degenerate states for the Hamiltonian [Formula: see text] at x = ± 1 for spin 1 that was given by Happer et al.1,2 to interpret the curious degeneracies of the Zeeman effect for condensed vapor of 87 Rb . The operators obey Yangian commutation relations. We show that the curious degeneracies seem to verify the Yangian algebraic structure for quantum tensor space and are consistent with the representation theory of Y(sl(2)).

Notizen: The Dipole Moment Function of HF Molecule Using Morse Potential

1977 ◽  
Vol 32 (8) ◽  
pp. 897-898 ◽  
Author(s):  
Y. K. Chan ◽  
B. S. Rao
Keyword(s):  
Wave Equation ◽  
Dipole Moment ◽  
Potential Function ◽  
Electric Dipole ◽  
Morse Potential ◽  
Moment Function ◽  
Matrix Elements ◽  
The Matrix ◽  
Vibration Rotation ◽  
Experimental Values

Abstract The radial Schrödinger wave equation with Morse potential function is solved for HF molecule. The resulting vibration-rotation eigenfunctions are then used to compute the matrix elements of (r - re)n. These are combined with the experimental values of the electric dipole matrix elements to calculate the dipole moment coefficients, M 1 and M 2.

Causal amplitudes and the Yang-Feldman formalism

1957 ◽  
Vol 53 (4) ◽  
pp. 843-847 ◽  
Author(s):  
J. C. Polkinghorne
Keyword(s):  
Field Theory ◽  
Green’S Functions ◽  
Free Field ◽  
Dispersion Relations ◽  
Matrix Elements ◽  
Field Equations ◽  
Commutation Relations ◽  
The Matrix ◽  
Free Fields ◽  
Set Up

ABSTRACTThe Yang-Feldman formalism vising the Feynman-like Green's functions is set up. The corresponding free fields have non-trivial commutation relations and contain information about the scattering. S-matrix elements are simply the matrix elements of anti-normal products of the field φF′(x). These are evaluated, and they give directly expressions used in the theory of causality and dispersion relations. It is possible to formulate field theory in a form in which the fields obey free field equations and the effects of interaction are contained in their commutation relations.

The Dipole Moment Function of H79Br Molecule

1972 ◽  
Vol 27 (11) ◽  
pp. 1563-1565 ◽  
Author(s):  
D. N. Urquhart ◽  
T. D. Clark ◽  
B. S. Rao
Keyword(s):  
Wave Equation ◽  
Dipole Moment ◽  
Potential Function ◽  
Electric Dipole ◽  
Morse Potential ◽  
Moment Function ◽  
Matrix Elements ◽  
The Matrix ◽  
Vibration Rotation ◽  
Experimental Values

Abstract The radial Schrödinger wave equation with Morse potential function is solved for H79Br molecule. The resulting vibration-rotation eigenfunctions are then used to compute the matrix elements of (r-re)n . These are combined with the experimental values of the electric dipole matrix elements to calculate the dipole moment coefficients, M1 and M2 .

A REALIZATION OF DYNAMIC GROUP FOR AN ELECTRON IN A UNIFORM MAGNETIC FIELD

2002 ◽  
Vol 11 (04) ◽  
pp. 265-271 ◽  
Author(s):  
SHISHAN DONG ◽  
SHI-HAI DONG
Keyword(s):  
Magnetic Field ◽  
Relativistic Electron ◽  
Uniform Magnetic Field ◽  
Wave Functions ◽  
Matrix Elements ◽  
Eigenvalues And Eigenfunctions ◽  
Radial Wave ◽  
Creation And Annihilation Operators ◽  
The Matrix ◽  
Analytical Expressions

The eigenvalues and eigenfunctions of the Schrödinger equation with a non-relativistic electron in a uniform magnetic field are presented. A realization of the creation and annihilation operators for the radial wave-functions is carried out. It is shown that these operators satisfy the commutation relations of an SU(1,1) group. Closed analytical expressions are evaluated for the matrix elements of different functions ρ2 and [Formula: see text].

New analytical expression for the rotational factor in Raman transitions

1995 ◽  
Vol 73 (9-10) ◽  
pp. 559-565 ◽  
Author(s):  
M. Korek ◽  
H. Kobeissi
Keyword(s):  
Direct Calculation ◽  
Matrix Elements ◽  
Numerical Application ◽  
Raman Transitions ◽  
The Matrix ◽  
Present Formalism ◽  
Vibration Wave ◽  
Schrödinger Perturbation ◽  
Analytical Expressions ◽  
Rotational Factor

The matrix elements of the polarizability anisotropy γ in the Raman spectra of diatomic molecules are investigated. These matrix elements are given by [Formula: see text] where Gνν′(m) is the rotational factor with m = [(J′(J′ + 1) − J(J + 1)]/2 and J′ − J = ±2. By using a nonconventional approach to the Rayleigh–Schrödinger perturbation theory the rotational factor can be written as Gνν′(m) = A0 + A1m + A2m2 where the coefficients A0, A1, and A2 are given by simple analytical expressions in terms of the integrals [Formula: see text] and [Formula: see text] where Y stands for Ψ(0) (the pure vibration wave function), or Ψ(0) (the first rotational perturbative correction to Ψ(0), or Ψ(2) (the second correction). A numerical application is presented for the ground states of CO and H2 molecules. A comparison with a numerical and direct calculation of the rotational factor Gνν′(m) shows the accuracy of the present formalism.

scholarly journals SPIN-POLARIZED PHOTOCURRENT THROUGH QUANTUM DOT PHOTODETECTOR

2017 ◽  
Vol 24 (1&2) ◽  
pp. 7-13
Author(s):  
Nguyen Van Hieu ◽  
Nguyen Bich Ha
Keyword(s):  
Quantum Dot ◽  
Electron Tunneling ◽  
Electronic Transitions ◽  
Matrix Elements ◽  
Semiconductor Quantum Dot ◽  
Spin Polarized ◽  
The Matrix ◽  
Electron Photon ◽  
Analytical Expressions ◽  
Polarized Photons

The theory of the photocurrent through the photodetector based on a two-level semiconductor quantum dot (QD) is presented. The analytical expressions of the matrix elements of the electronic transitions generated by the absorption of the circularly polarized photons are derived in the lowest order of the perturbation theory with respect to the electron tunneling interaction as well as the electron-photon interaction. From these expressions the mechanism of the generation of the spin-polarized of electrons in the photocurrent is evident. It follows that the photodetector based on the two-level semiconductor QD can be used as the model of a source of highly spinpolarized electrons.

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