Non-perturbative energy expressions for the generalized anharmonic oscillator

Abstract

A general expression for the energy eigenvalues of an anharmonic oscillator characterized by the potential ½(m2x2)+x2 ( > 0) has been derived non-perturbatively. For quartic ( = 2), sextic ( = 3) and octic ( = 4) anharmonic oscillators, over a wide range of n and , these energy values agree well with the numerical values calculated by earlier workers.

Octic Anharmonic Oscillators: Perturbed Coherent States and the Classical Limit

“…Now, using (25) in (23) we find the perturbed wave function |ψ n up to the first order in the parameter λ as follows…”

“…The quartic anharmonic oscillator is the archetypal model that has been used over and over to serve this purpose [13][14][15][16][17][18][19][20][21][22]. There are also several investigations concerning the higher order and general anharmonic oscillators [23][24][25][26][27][28][29][30][31][32][33]. We mention also a small number of papers using anharmonic oscillators to investigate the classical-quantum connections; the classical limit of the quartic anharmonic oscillator is discussed in [34] and [35], and that of the sextic anharmonic oscillator in [36].…”

Effects of Intense Laser Field on Electronic and Optical Properties of Harmonic and Variable Degree Anharmonic Oscillators

“…Additionally, why standard RS perturbation theory does not work for an AHO is explained in detail in this paper. The AHO potentials with sextic, octic, etc., terms have also been studied extensively [ 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 ] since these potentials play an important role in the quantum tunneling time problems, and in the spectra of molecules. In this context, the electronic and optical properties of the HO and single and double anharmonic oscillators, including higher-order anharmonic terms such as the quartic and sextic under the non-resonant intense laser field, are investigated in this paper by changing the structural parameters and field intensity.…”

Study of continuous variable entanglement in coupled oscillator systems by means of the dynamical two-step approach

“…[40] have introduced several convergent algorithms which are able to calculate the eigenvalues of anharmonic oscillators depending on the magnitude of the coupling constant. Sharma and Fiase [41] have worked out an analytical expression for the energy eigenvalues of oscillators with an even-order of anharmonicities, while Datta and Rampal [42] have studied analytically the wave function and excited energy levels of doubly anharmonic oscillators in the asymptotic regime. Moreover, there is a technique known as the Lanczos iteration method [43,44] which yields fast converging results for both the eigenvalues and eigenvectors, but requires a pre-allocation of an appropriate trial wave function.…”

“…As an important model in physics, quantum oscillator has been studied extensively in the past [39,40,41,42,48,49,50,51,52]. Motivated by its application to molecular physics and quantum field theory, researchers begin to investigate the consequences and effects of interaction within a system of coupled oscillators.…”