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1.
Using an algebraic technique based on the Lie algebra of the group SO(2, 1) the eigenvalues of the triple-well anharmonic
oscillator are calculated for all ranges of the coupling constant. Approximate analytic formulas for the eigenvalues up to
second order are given. The results obtained are compared with those of other authors. 相似文献
2.
Nazakat Ullah 《Pramana》1993,41(2):C201-C202
It is pointed out that the value of the perturbed energy calculated in the comment by Rath and Pattnayak, is incorrect. When
the coupling parameter has the value unity, the energy up to second order of perturbation theory is 0.801 compared to its
exact value of 0.804. The suggested split of the Hamiltonian into an unperturbed and perturbed part does not seem to be of
any use as the unperturbed part contains anharmonic terms. 相似文献
3.
In this paper we present explicit and simple analytical formulae for the energy eigenvaluesE
n (λ) of one-dimensional anharmonic oscillators characterized by the potentials 1/2mω
2
x
2+λx
2α withα=2, 3 and 4. A simple intuitive criterion supplemented by the requirement of correct asymptotic behaviour, has been employed
in arriving at the formulae. Our energy values over a wide range ofn andλ are in good agreement with the numerical values computed by earlier workers through very elaborate techniques. To our knowledge
this is the first time that formulae of such wide validity have been given. The results for pure power oscillators are trivially
obtained by going over to theω→0 limit. Approximate analytic expressions for the low order even moments ofx are also given. 相似文献
4.
We investigate the role played by the molecules as quantum oscillators in a diatomic gasdynamic laser by considering quasi-harmonic behaviour within the context of one-dimensional quantum anharmonic oscillators. Vibrational energy levels depending upon a parameter relative to anharmonicity are discussed in terms of the values taken on by this parameter and the values taken on by the vibrational quantum number. 相似文献
5.
Carl M. Bender Fred Cooper Gerald Guralnik Harvey A. Rose David H. Sharp 《Journal of statistical physics》1980,22(6):647-660
We discuss the simple, randomly driven systemdx/dt = –x –x3 +f(t), wheref(t) is a Gaussian random function or stirring force with f(t)f(t) = (t – t). We show how to obtain approximately the coefficients of the expansion of the equal-time Green's functions as power series in (1/R)n, whereR is the internal Reynolds number ()1/2/, by using a new expansion for the path integral representation of the generating functional for the correlation functions. Exploiting the fact that the action for the randomly driven system is related to that of a quantum mechanical anharmonic oscillator with Hamiltonianp
2/2 +m
2
x
2/2 +vx
4 +x
6/2, we evaluate the path integral on a lattice by assuming that thex
6 term dominates the action. This gives an expansion of the lattice theory Green's functions as power series in 1/(a)1/3, wherea is the lattice spacing. Using Padé approximants to extrapolate toa = 0, we obtain the desired large-Reynolds-number expansion of the two-point function.Supported financially by the National Science Foundation and the U.S. Department of Energy. 相似文献
6.
Comment on: Modified perturbation series for the anharmonic oscillator using linearization technique
Following the argument of Halliday and Suranyi (1980), we find that the perturbation series for the anharmonic oscillator
using linearization technique of random phase approximation (Ullah 1985) will lead to divergent result. A remedy for this
is also suggested. 相似文献
7.
On the basis of a radial generalization of the JWKB quantization rule, which incorporates higher orders of the approximation,
an explicit analytical formula is derived for the energy levels of the three-dimensional sextic anharmonic oscillator. The
formula exhibits the scaling property of the exact eigenvalues, and is readily generalized to any dimension. The predicted
results are in good agreement with known numerical values. 相似文献
8.
Nazakat Ullah 《Pramana》1985,24(1-2):27-29
The linearization technique of random phase approximation is applied to the anharmonic oscillator to find a modified perturbation
series. It is shown that for the anharmonic termλx
4, the ground state energyE
0 upto the second order of perturbation is given byE
0=(35/48) (3/4)1/3
λ
1/3 asλ→∞. 相似文献
9.
Yu. M. Poluéktov 《Russian Physics Journal》2009,52(1):33-45
A modified perturbation theory is formulated for an asymmetric anharmonic oscillator based on a choice of the main approximation
constructed by analogy with the self-consistent field model. This perturbation theory has a much wider range of application
in comparison with the standard approach and considers a finite number of energy levels in the potential well already in the
main approximation. This approach is used for the construction of a two-atomic model of a quantum crystal. A quantum analog
of the Lindeman criterion is obtained.
Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 30–40, January, 2009. 相似文献
10.
利用Kinani-Daoud方法构造了非谐振子势的Gazeau-Klauder(GK)相干态和Klauder-Perelomov(KP)相干态,表明两种相干态在非线性谐振子势下具有完全不同的形式,并对两种相干态的完备性以及各自构成的Hilbert空间进行了讨论. 对相干态的Mandel Q参数的研究表明:GK相干态服从亚Poisson统计分布,KP相干态服从超Poisson统计分布.
关键词:
非谐振子
Gazeau-Klauder相干态
Klauder-Perelomov相干态 相似文献
11.
12.
Using the path-integral technique, we derive here the large-quantum-number behaviour of energy eigenvalues of a coupled anharmonic oscillator. The result clearly shows the behaviour of the leading and the next to leading term with respect to the parameters contained in the coupled anharmonic part of the potential. 相似文献
13.
This is the third article in a series of three papers on the resonance energy levels of anharmonic oscillators. Whereas the first two papers mainly dealt with double-well potentials and modifications thereof [see J. Zinn-Justin, U.D. Jentschura, Ann. Phys. (N.Y.) 313 (2004) 197 and 269], we here focus on simple even and odd anharmonic oscillators for arbitrary magnitude and complex phase of the coupling parameter. A unification is achieved by the use of PT-symmetry inspired dispersion relations and generalized quantization conditions that include instanton configurations. Higher-order formulas are provided for the oscillators of degrees 3 to 8, which lead to subleading corrections to the leading factorial growth of the perturbative coefficients describing the resonance energies. Numerical results are provided, and higher-order terms are found to be numerically significant. The resonances are described by generalized expansions involving intertwined nonanalytic exponentials, logarithmic terms and power series. Finally, we summarize spectral properties and dispersion relations of anharmonic oscillators, and their interconnections. The purpose is to look at one of the classic problems of quantum theory from a new perspective, through which we gain systematic access to the phenomenologically significant higher-order terms. 相似文献
14.
Population distribution is studied quantitatively for a diatomic gasdynamic laser in which the molecules behave as strongly anharmonic oscillators under the action of a Morse internuclear potential. In fact, mathematical relationships concerning the two fundamental parameters associated with anharmonicity are derived. 相似文献
15.
Generation-channel interference of high-order harmonics of an anharmonic oscillator driven by bi-chrime laser fields and its mechanism
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A method to describe the generation channels of high-order harmonics is proposed.According to this method,the mechanism of generation-channel interference of high-order harmonics is revealed clearly.We take the anharmonic oscillator driven by bi-chrome fields as an example to illustrate that this method can be used to understand the effect of generation-channel interference. 相似文献
16.
Recently, a nonlinear master equation has been suggested to account for the effect of diffusion in the fluctuations of nonlinear systems away from equilibrium. An asymptotic expansion of the solutions of this master equation in the inverse of the diffusion constant is presented. The applicability of the method is illustrated with several examples of model chemical reactions. 相似文献
17.
18.
19.
To make sense of quantum field theory in an arbitrary (globally hyperbolic) curved spacetime, the theory must be formulated
in a local and covariant manner in terms of locally measurable field observables. Since a generic curved spacetime does not
possess symmetries or a unique notion of a vacuum state, the theory also must be formulated in a manner that does not require
symmetries or a preferred notion of a “vacuum state” and “particles”. We propose such a formulation of quantum field theory,
wherein the operator product expansion (OPE) of the quantum fields is elevated to a fundamental status, and the quantum field
theory is viewed as being defined by its OPE. Since the OPE coefficients may be better behaved than any quantities having
to do with states, we suggest that it may be possible to perturbatively construct the OPE coefficients—and, thus, the quantum
field theory. By contrast, ground/vacuum states—in spacetimes, such as Minkowski spacetime, where they may be defined—cannot
vary analytically with the parameters of the theory. We argue that this implies that composite fields may acquire nonvanishing
vacuum state expectation values due to nonperturbative effects. We speculate that this could account for the existence of
a nonvanishing vacuum expectation value of the stress-energy tensor of a quantum field occurring at a scale much smaller than
the natural scales of the theory.
Fourth Award in the 2008 Essay Competition of the Gravity Research Foundation. 相似文献
20.
We investigate the change in the calculated value of asymptotic normalization constant (ANC) by the hyperspherical harmonics
expansion method with the inclusion of three nucleon force (3BF) in addition to two nucleon force. We see that ANC does not
change very much with the inclusion of 3BF indicating that the 3BF does not alter the asymptotic behaviours of HHE wavefunction
significantly. 相似文献