同调谐振子谱空间上的对称性和参量双粒子模型

研究了同调谐振子谱空间上的对称性，通过适当的参量代换给出形象的图示. 得到归一化的本征函数解析表达式， 并证明了线性谐振子是同调谐振子的退化. 揭示出同调谐振子是参量双粒子模型，并给出该模型的相干态，该相干态自动包含用Glauber相干态构 造的奇、偶相干态. 关键词： 同调谐振子 赝角动量方法 本征值谱 本征函数 参量双 光子模型     

用Riccati变换求解同调谐振子

利用Riccati变换求解同谐谐振子的定态薛定谔方程,求得了能谱及态函数 关键词： 同调谐振子 本征值谱 Riccati变换法     

同调谐振子参数与基态能量的关系

采用升降算符方法研究了同调谐振子(包括一维谐振子)定态薛定谔方程的严格解,详细讨论了谐振子参量不同取值范围形成不同基态能量的关系.对于有关文献的一些欠完善的提法给予了分析和澄清 关键词： 同调谐振子 升算符 降算符 基态能量     

同调谐振子的变形

实现了在保持本征值谱结构不变情况下同调谐振子的几种变形.这些变形包括三维各向同性谐振子径向方程、开普勒径向方程、Morse势s态等问题.每一个变形体系对应着同调参量g的确定取值.同调谐振子有一定的普遍适应性,具有丰富的内容. 关键词： 同调谐振子 同调参量 产生算符 湮没算符     

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.     

超对称准经典近似和本征值问题

运用超对称准经典近似方法给出三维谐振子、氢原子的能谱,进而将该方法用于含角坐标的二阶微分方程,得到角动量平方L2的本征值和非中心势的角向本征值.     

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.     

粒子数表象中的谐振子

用二次量子化方法讨论一维线性谐振子能量本征值,并将结果用于解决磁场中带电粒子的能量本征值和角动量平方算符的本征值问题。     

双参数形变谐振子湮没算符高次幂本征态的反聚束效应

研究了双参数形变谐振子湮没算符高次幂(akqs,k≥3)本征态的反聚束效应,并就k=3的情况运用数值计算方法研究了双参数形变对该效应的影响.结果表明,在双参数形变相干态中谐振子强度x=｜α｜²的若干取值区间内,akqs的本征态均可呈现反聚束效应,并且明显地受到qs形变参数的影响.     

一种简捷求解定态薛定谔方程的方法:科尔-霍普夫变换法

介绍一种求解各个能级及定态波函数的简捷方法,即借助于科尔-霍普夫(Cole-Hopf)变换法,将给定势函数的定态薛定谔方程变换成黎卡提(Riccati)方程,以求出各个能级及定态波函数.并以谐振子、球谐振子、氢原子、P schl-Teller势、Morse势、Hulth啨n势、双原子分子的三参量势函数、同调谐振子为实例,给出求解方法及结果.     

Dirac Oscillator Under the New Generalized Uncertainty Principle From the Concept Doubly Special Relativity

We discuss one-dimensional Dirac oscillator, by using the concept doubly special relativity. We calculate the energy spectrum by using the concept doubly special relativity. Then, we derive another representation that the coordinate operator remains unchanged at the high energy while the momentum operator is deformed at the high energy so that it may be bounded from the above. Actually, we study the Dirac oscillator by using of the generalized uncertainty principle version and the concept doubly special relativity.     

A concise quantum mechanical treatment of the forced damped harmonic oscillator

By selecting a right generalized coordinate X, which contains the general solutions of the classical motion equation of a forced damped harmonic oscillator, we obtain a simple Hamiltonian which does not contain time for the oscillator such that Schrödinger equation and its solutions can be directly written out in X representation. The wave functin in x representation are also given with the help of the eigenfunctions of the operator \(\hat X\) in x representation. The evolution of \(\left\langle {\hat x} \right\rangle \) is the same as in the classical mechanics, and the uncertainty in position is independent of an external influence; one part of energy mean is quantized and attenuated, and the other is equal to the classical energy.     

Mutual transformations between the P–Q,Q–P,and generalized Weyl ordering of operators

Based on the generalized Weyl quantization scheme, which relies on the generalized Wigner operator Ok （p, q） with a real k parameter and can unify the P-Q, Q-P, and Weyl ordering of operators in k = 1, - 1,0, respectively, we find the mutual transformations between 6 （p - P） （q - Q）, （q - Q） 3 （p - P）, and （p, q）, which are, respectively, the integration kernels of the P-Q, Q-P, and generalized Weyl quantization schemes. The mutual transformations provide us with a new approach to deriving the Wigner function of quantum states. The - and - ordered forms of （p, q） are also derived, which helps us to put the operators into their - and - ordering, respectively.     

A generalized Collins formula derived by virtue of the displacement-squeezing related squeezed coherent state representation

Based on the displacement-squeezing related squeezed coherent state representation ≤ft\vert z\right\rangle _{g} and using the technique of integration within an ordered product of operators, this paper finds a generalized Fresnel operator, whose matrix element in the coordinate representation leads to a generalized Collins formula (Huygens--Fresnel integration transformation describing optical diffraction). The generalized Fresnel operator is derived by a quantum mechanical mapping from z to sz-rz^{\ast } in the % ≤ft\vert z\right\rangle _{g} representation, while ≤ft\vert z\right\rangle _{g} in phase space is graphically denoted by an ellipse.     

A generalized Weyl—Wigner quantization scheme unifying P-Q and Q-P ordering and Weyl ordering of operators

By extending the usual Wigner operator to the s-parameterized one as 1/4π2 integral (dyduexp [iu(q-Q)+iy(p-P)+is/2yu]) from n=- ∞ to ∞ with s beng a,real parameter,we propose a generalized Weyl quantization scheme which accompanies a new generalized s-parameterized ordering rule.This rule recovers P-Q ordering,Q-P ordering,and Weyl ordering of operators in s = 1,1,0 respectively.Hence it differs from the Cahill-Glaubers’ ordering rule which unifies normal ordering,antinormal ordering,and Weyl ordering.We also show that in this scheme the s-parameter plays the role of correlation between two quadratures Q and P.The formula that can rearrange a given operator into its new s-parameterized ordering is presented.     

New Convenient Way for Deriving Exponential Operators＇ Disentangling Formulas and Their Applications

We recommend a new convenient method for disentangling some exponential operators and derive a set of new operator identities. Especially, we derive the normal odering form of exp [fa^＋a ＋ ga^2＋ ＋ ka^2] without appealing to Lie algebra method. Application of these formulas in solving some dynamic Hamiltonian is presented.     

Operator Formulas Involving Generalized Stirling Number Derived by Virtue of Normal Ordering of Vacuum Projector

By virtue of the normal ordering of vacuum projector we directly derive some new complicated operator identities, regarding to the generalized Stirling number.     

Geometric phases and Mielnik's evolution loops

The cyclic evolutions and associated geometric phases induced by time-independent Hamiltonians are studied for the case when the evolution operator becomes the identity (those processes are called evolution loops). We make a detailed treatment of systems having equally-spaced energy levels. Special emphasis is made on the potentials which have the same spectrum as the harmonic oscillator potential (the generalized oscillator potentials) and on their recently found coherent states.     

类氢原子的相干态

用赝角动量算符方法直接求解球坐标下束缚态类氢原子的径向方程.给出本征态的解析表达式,其中归一化问题比较特殊,需要格外细致;最后给出相应的相干态. 关键词： 类氢原子径向方程 赝角动量算符方法 本征值谱 相干态