共查询到20条相似文献,搜索用时 46 毫秒
1.
Harald J. W. Müller 《Zeitschrift für Physik A Hadrons and Nuclei》1967,205(2):149-158
A modified Rayleigh-Schrödinger perturbation method is used to derive explicit expansions for the eigenvalues and eigensolutions of the anharmonic oscillator. We then point out the dual relationship between the anharmonic oscillator and the Schrödinger equation for a Yukawa potential. Finally we consider an application of the method to a field-theoretic Hamiltonian, since the anharmonic oscillator plays a dominant role in many field-theoretic models. 相似文献
2.
Biswanath Rath 《Fortschritte der Physik》1991,39(7):491-499
It is observed that variationally calculated wavefunctions do not satisfy orthogonality relation when tested for the potentials like anharmonic oscillator and deviated hydrogen atom type. A new approach is suggested using quasi-states only to correlate between variationally calculated wavefunctions and orthogonality relation using perturbation theory considering the anharmonic oscillator example. Analytically expression for energy levels of the anharmonic oscillator are calculated up to the second order. A test for convergency of the perturbation theory is also discussed. 相似文献
3.
Some remarkable arithmetic properties of the anharmonic oscillator are considered. The concept of the p-adic summability is discussed. For the ground-state energy of the anharmonic oscillator the p-adic summability is shown. 相似文献
4.
The present review is devoted to the study of certain aspects of anharmonic, time-dependent and damped oscillator(s) system using different theoretical techniques. A theoretical understanding of these systems is important for application in many problems in physics, mechanics and other fields. We discuss in detail the difficulties in the theoretical analysis of the problem. In particular we discuss here the regular, well-behaved perturbative solution, the large quantum number behaviour of anharmonic oscillator(s) using the technique of coherent states, exact solution of quantum anharmonic oscillators, the electromagnetic radiation emitted by a charged particle executing damped anharmonic oscillator motion using Krylov-Bogoliubov approximation method, use of invariants to obtain solution and coherent states of time-dependent oscillator(s), the derivation of perturbative frequencies of a damped coupled anharmonic oscillators system using suitable canonical transformation in the framework of Hamilton-Jacobi formalism and the quantisation and construction of coherent states of a damped oscillator using time-dependent operators. 相似文献
5.
Y. Ben-Aryeh 《Journal of Quantitative Spectroscopy & Radiative Transfer》1980,23(4):403-409
A model of multiphoton absorption of i.r. laser radiation by an anharmonic, molecular, vibrational mode is discussed. The multiphoton absorption is described as a stochastic process for which the reservoir, including rotation and other vibrational modes, modulates the frequency of the active oscillator stochastically. The treatment of the nonlinear oscillator is based on quantization of a classical, driven anharmonic oscillator. 相似文献
6.
R. D. Khan Zhang Jialun Ding Sheng Shen Wenda 《International Journal of Theoretical Physics》1993,32(11):2023-2029
The exact solution to a velocity-dependent quantum forced anharmonic oscillator is derived by using integral operators and an iteration method. The study is carried out in operational form by use of the creation and annihilation operators of the oscillator. The time development of the displacement and momentum operators of the anharmonic oscillator is given. These operators are presented as a Laplace transform and a subsequent inverse Laplace transform of suitable functionals. 相似文献
7.
运用积分算子和迭代方法求得了依赖于速度的量子受迫非简谐振子的精确解。给出了非简谐振子坐标和动量算符的时间演化。这些算符被表示成适当泛函的拉普拉斯变换及随后的逆拉普拉斯交换的形式。
关键词: 相似文献
8.
An excited anharmonic oscillator is considered under conditions of adiabatic (i.e., slow, as compared to the oscillation period) loading with an external force tending to a constant value at long times. The energy characteristics of the adiabatically loaded anharmonic oscillator, such as the instantaneous energy of the oscillator, the maximum kinetic (oscillation) energy, and the kinetic and potential energies averaged over the period, are analytically calculated as a function of the steady-state force. The analytical results are confirmed by the data of numerical calculations. It is established that the external force gives rise to a redistribution of the average kinetic and potential components of the initial energy of the anharmonic oscillator and that the transferred energy portions at a small external force considerably exceed the average work done by the external force. 相似文献
9.
10.
将几何相位理论应用于非同调谐振子(isotonic oscillator缩写为IO)这类量子系统,运用算符分解方法计算了系统在二态体系的Aharonov-Anandan相位,推广至三态及多态体系,并讨论了AA相位更普遍的计算公式和变化规律. 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.
Hans Maassen 《Journal of statistical physics》1984,34(1-2):239-261
A quantum-mechanical treatment of the evolution of an anharmonic oscillator coupled to a heat bath is given. It is shown that for a certain class of anharmonic potentials the heat bath drives the oscillator to an equilibrium state, close to the quantum Gibbs state associated to the potential. Thus a partial proof is provided for a conjecture of R. Benguria and M. Kac.This paper contains part of the author's Ph.D. work, done at the Institute for Theoretical Physics of Groningen State University, Groningen, the Netherlands. 相似文献
14.
The two-dimensional hydrogen with a linear potential in a magnetic field is solved by two different methods. Furthermore the connection between the model and an anharmonic oscillator is investigated by methods of KS transformation. 相似文献
15.
《Infrared physics》1989,29(2-4):485-501
The quantum dynamics of molecular vibrations under the influence of coherent infrared-laser multiphoton excitation is irregular, in most cases, on the time scale of experimental interest. This irregularity arises from the anharmonic nature of the molecular force fields and is already present in one dimensional anharmonic oscillators. We analyse the onset of the irregularity in the model of a Morse oscillator and discuss the role of statistical or “chaotic” behaviour of the time dependent probability density. We further discuss the role of direct multiphoton excitation in these multilevel systems and compare the results with exact solutions for the harmonic oscillator. 相似文献
16.
A perturbation theory model that describes splitting of the spectra in highly symmetrical molecular species in electrostatic field is proposed. An anahrmonie model of a two-dimensional oscillator having Kratzer potential energy function is used to model the molecular species and to represent the unperturbed system. A selection rule for the radial quantum number of the oscillator is derived. The eigenfunctions of a two-dimensional anharmonic oscillator in cylindrical coordinates are used for the matrix elements representing the probability for energy transitions in dipole approximation to be calculated. Several forms of perturbation operators are proposed to model the interaction between the polyatomic molecular species and an electrostatic field. It is found that the degeneracy is removed in the presence of the electric field and spectral splitting occurs. Anharmonic approximation for the unperturbed system is more accurate and reliable representation of a reaJ polyatomic molecular species. 相似文献
17.
《Physics letters. A》2006,359(4):272-274
We discuss alternative perturbation expansions for partially solvable quantum-mechanical models. We consider a sextic anharmonic oscillator as a particular example. 相似文献
18.
The behavior of an anharmonic quantum oscillator in a harmonic external electric field is examined. The quasienergy is calculated
numerically as a function of the field parameters (intensity and frequency) for highly excited states. It depends in complex
fashion on frequency and field intensity near resonance. Quasi-intersection of levels is observed in a broad range of quantum
numbers. These effects are manifestations of dynamic chaos in highly excited states of an anharmonic oscillator in an external
field.
Omsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 11–18, February, 1998. 相似文献
19.
S. K. Bose 《Letters in Mathematical Physics》1979,3(4):259-264
We obtain here a perturbative solution of the generalx
2q+2
anharmonic damped oscillator in the coherent state representation. The solution does not contain any secular term and shows, explicitly, the damping and the anharmonic effects. 相似文献
20.
It has been shown that, in a classical ensemble of anharmonic oscillators, the mean value of the oscillator coordinate is a classical parameter in the sense that the statistical sum of the ensemble satisfies, to the second order in the anharmonicity constant, the stationary condition with respect to this parameter. This stationary condition is equivalent to the classical condition for the balance of external and internal forces acting on the oscillator. This equivalence is justified by the fact that the statistical sum, which is stationary with respect to the mean oscillator coordinate, agrees within this accuracy with the usual statistical sum of independent anharmonic oscillators. After introducing the classical parameter into a large thermodynamic system, the energy balance under the mechanical deformation of the system is realized through the exchange between two scale levels: the energy of oscillations at the microlevel and the macroscopic potential energy of deformation of the sample as a whole. 相似文献