几类宏观量子态的内部结构及其压缩特性

谐振子,变形振子,非简谐振子以及变形非简谐振子湮没算符高次幂的正交归一本征态都具有奇偶结构形式.正是由于这种结构特点决定了它们振幅的高次幂压缩性质.     

Q形变的非简谐振子广义相干态

利用变换算符导出了Q形变的非简谐振子代数,由此得到Q形变的非简谐振子广义相干态．这些状态具有过完备性,是Q形变的自然算符的极小测不准状态．在主压缩区间中偶相干态的相对压缩率随形变程度的增大而增大．     

Q形变的非简谐振子广义相干态

利用变换算符导出了Q形变的非简谐振子代数,由此得到Q形变的非简谐振子广义相干态.这些状态具有过完备性,是Q形变的自然算符的极小测不准状态.在主压缩区间中偶相干态的相对压缩率随形变程度的增大而增大.     

q变形非简谐振子湮没算符高次幂本征态的反聚束特性

研究了q变形非简谐振子湮没算符高次幂本征态的反聚束特性,并用数值计算方法定量研究了变形参量q对这一特性的影响.结果表明,q变形非简谐振子湮没算符高次幂本征态在非谐振子强度x│=β│²的若干取值区间内可多次交替地呈现反聚束效应,并且变形参量q对这一效应有很大的影响.     

非简谐振子湮灭算符高次幂bN-本征态的量子统计性质

本文了研究了非简谐振子湮灭算符高次幂ｂ＾Ｎ－（Ｎ≥２）本征态的量子统计性质。     

三维各向同性谐振子波函数的递推关系(英文)

本文应用拉普拉斯变换得到了三维各向同性谐振子波函数边界的精确解,同时,利用同种方法还得到了利用产生算符和湮灭算符表达的该波函数的递推关系.     

Q变形非简谐振子湮没算符高次幂本征态的反聚束效应

引入了一种量子反聚束效应,研究了Q变形非简谐振子湮没算符K次幂(K≥3)的K个本征态的量子反聚束效应,探讨了这些本征态的物理意义.结果表明,这K个本征态均可呈现量子反聚束效应,它们都可由不同时刻依赖于时间的Q变形非简谐振子广义相干态的线性叠加而生成.     

非简谐振子湮灭算符三次幂的本征态及其性质

构造了非简谐振子湮灭算符３次幂的正交归一本征态，证明它是光场振幅的３ｎ次幂的最小测不准态，无压缩效应，并研究了它的反聚束性质。     

线性谐振子的非定态波函数

引入初坐标算符和初动量算符为线性谐振子的力学量完全集，求解薛定谔方程，可得到线性谐振子的两类非定态波函数。     

线性谐振子的非定态波函数

引入初坐标算符和初动量算符为线性谐振子的力学量完全集，求解薛定谔方程，可得到线性谐振子的两类非定态波函数．     

Evolution of a velocity-dependent quantum forced anharmonic oscillator

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.     

Classical and quantum oscillators of quartic anharmonicities: second-order solution

An analytical solution up to the second order in the coupling constant λ is obtained for a classical quartic anharmonic oscillator by using Taylor series method. Our solution yields, as a special instance, the corresponding results obtained by using Laplace transform. With the help of correspondence principle, the classical solution is used to obtain the solution corresponding to a quantum quartic anharmonic oscillator. In the weak coupling regime (i.e., anharmonic constant λ⪡1), the so-called secular terms in classical and quantum solutions are tucked in (summed up) to avoid the nonconvergence. Both the classical and quantum solutions are used to obtain the frequency shifts of the quartic oscillators. It is found that these frequency shifts coincide exactly with those of the earlier results obtained by other methods. From the quantum field theoretic point of view, our solution exhibits the so-called Lamb shift. As an application of the solution for the quantum oscillator, we examine the possibility of getting squeezed states out of the input coherent light interacting with a nonlinear medium of inversion symmetry.     

Exact solutions of the Klein—Gordon equation with ring-shaped oscillator potential by using the Laplace integral transform

We present exact solutions for the Klein-Gordon equation with a ring-shaped oscillator potential. The energy eigenvalues and the normalized wave functions are obtained for a particle in the presence of non-central oscillator potential. The angular functions are expressed in terms of the hypergeometric functions. The radial eigenfunctions have been obtained by using the Laplace integral transform. By means of the Laplace transform method, which is efficient and simple, the radial Klein-Gordon equation is reduced to a first-order differential equation.     

Unified Method for Dynamical Groups of Some Anharmonic Potentials

Realizations of the creation and annihilation operators for some important anharmonic potentials, such as the Morse potential, the modified Pöschl–Teller potential (MPT), the pseudoharmonic oscillator, and infinitely deep square-well potential, are presented by a factorization method. It is shown that the operators for the Morse potential and the MPT potential satisfy the commutation relations of an SU(2) algebra, but those of the pseudoharmonic oscillator and the infinitely deep square-well potential constitute an SU(1, 1) algebra. The matrix elements of some related operators are analytically obtained. The harmonic limits of the SU(2) operators for the Morse and MPT potentials are studied as the Weyl algebra.     

Splitting of Spectra in Anharmonic Oscillators Described by Kratzer Potential Function

A perturbation theory model that describes splitting of the spectra in highly symmetrical molecular species in electrostatic field is proposed. An anahrmonic model of a two-dimensional oscillator having Kratzer potential energy functionis 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 interactionbetween 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 real polyatomic molecular species.     

On the anharmonic oscillator in quantum mechanics and in field theory

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.     

A model for a stochastic multiphoton absorption process of an anharmonic oscillator

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.     

On the p-adic summability of the anharmonic oscillator

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.     

Energy features of an adiabatically loaded anharmonic oscillator

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.