Uncertainty products for the anharmonic morse oscillator (original) (raw)
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Generalized and Gaussian coherent states for the Morse potential
Journal of Physics A: Mathematical and Theoretical, 2008
In this paper, we will consider one-dimensional anharmonic oscillator, which represents well the anharmonic vibrations in diatomic molecules. For the description of the associate potential we shall use the Morse potential, which gives a good approximation of the experimentally observed vibrational modes of molecules and hence contributes to the realistic description of the spectrum of diatomic molecules. Generalized and gaussian coherent states are thus constructed and compared in terms of the localisation of the particle in those states. We apply these results to the example of the sodium chloride molecule 1 H 35 Cl.
Gazeau–Klauder quasi-coherent states for the Morse oscillator
Physics Letters A, 2003
In the Letter, we have constructed and investigated some properties of the Gazeau-Klauder quasi-coherent states for the Morse potential, previously deduced by Roy and Roy. We have focused our attention on the thermal states and we have found the analytical form for the diagonal P -representation of the density operator.
The algebraic approach to the Morse oscillator
Journal of Physics A: Mathematical and General, 1980
The eigenfunctions and eigenvalues of the Schrödinger equation with a ring-shaped non-spherical oscillator are obtained. A realization of the ladder operators for the radial wave functions is studied. It is found that these operators satisfy the commutation relations of an SU(1, 1) group. The closed analytical expressions for the matrix elements of different functions ρ and ρ d dρ with ρ = r 2 are evaluated. 2004 Published by Elsevier B.V.
Quasi-bound states of coupled Morse oscillators
Chemical Physics Letters, 1985
Two different methods for approximating these as local&d states are compared. The algebraic approach is shown to be in very good accord with-the other method which is formulated in coordinate space and hence is differential in character. For these highly excited states an intennul~plet mixing term is included in the algebraic Hamiltoniau + For the technical def?nit%on of "compact" and other group theoretic terms. see ref. [ 131. 0 009-2614/85/Z% 03.30 0 Ekevier Science Publishers B-V.
Physical Review A, 1996
A method for calculating the analytical solutions of the one-dimensional Schrödinger equation is suggested. A general discussion of the possible forms of the potentials and wave functions that are necessary to get the analytical solution is presented. In general, the analytical solutions appear in multiplets corresponding to the quantum number n of the harmonic oscillator. As an application, known solutions for the anharmonic oscillators are critically recalculated and a few additional results are found. Analytical solutions are also found for the generalized Morse oscillators.
Construction of the Barut–Girardello quasi coherent states for the Morse potential
Annals of Physics, 2013
h i g h l i g h t s • Construct the coherent states of the Barut-Girardello kind (BG-CSs) for the MO potential. • They fulfil all the conditions needed to a coherent state. • Present the Mandel parameter and Husimi's and P-quasi distribution functions. • All results tend to those for the one dimensional harmonic oscillator in its harmonic limit.
Vibrational resonance in the Morse oscillator
Pramana, 2013
We investigate the occurrence of vibrational resonance in both classical and quantum mechanical Morse oscillators driven by a biharmonic force. The biharmonic force consists of two forces of widely different frequencies ω and Ω with Ω ≫ ω. In the damped and biharmonically driven classical Morse oscillator applying a theoretical approach we obtain an analytical expression for the response amplitude at the low-frequency ω. We identify the conditions on the parameters for the occurrence of the resonance. The system shows only one resonance and moreover at resonance the response amplitude is 1/(dω) where d is the coefficient of linear damping. When the amplitude of the high-frequency force is varied after resonance the response amplitude does not decay to zero but approaches a nonzero limiting value. We have observed that vibrational resonance occurs when the sinusoidal force is replaced by a square-wave force. We also report the occurrence of resonance and anti-resonance of transition probability of quantum mechanical Morse oscillator in the presence of the biharmonic external field.
Exactly Solvable Modified Morse Potentials for Quantum-Mechanical Applications
Physica Scripta, 1999
The equilibrium quasiprobability density function W (ϑ, ϕ) of spin orientations in a representation (phase) space of the polar and azimuthal angles (ϑ, ϕ) (analogous to the Wigner distribution for translational motion of a particle) is given by a finite series of spherical harmonics in the spin number and their associated statistical moments so allowing one to calculate W (ϑ, ϕ) for an arbitrary spin system in the equilibrium state described by the canonical distributionρ = e −βĤ S /Tr(e −βĤ S). The system with HamiltonianĤ S = −γhH •Ŝ−BŜ 2 Z is treated as a particular example (γ is the gyromagnetic ratio, h is Planck's constant, H represents an external magnetic field and B represents an internal field parameter). For a uniaxial system withĤ S = −γhHŜ Z −BŜ 2 Z , the solution may be given in the closed form.