超球空间中广义角动量波函数

利用复变函数及高级超越函数的性质,得到了多维超球空间中广义解动量波函数的完备集,给出了多维超球空广义角动量的本征值,多维空间中平面波展开关系式及其它关系式。     

A crucial experiment on the quantum conditions in a field-free vector potential

An experiment is proposed in order to distinguish between two different sets of eigenfunctions of charged particles outside a constant magnetic flux tube. The two sets of eigenfunctions lead to different values of observable quantities like the kinetic angular momentum and electric currents which can be experimentally detected in a superconductor.     

Nyström Method for the Coulomb and Screened Coulomb Potentials

In this paper, we show that the simple Nyström method can yield very accurate eigenvalues and eigenfunctions not only for large principal quantum number but also for large angular momentum quantum number. We demonstrate that the furcation phenomenon emerging in the calculated eigenfunctions can be regarded as an indicator for the bad behavior of the integral equation and the unreliability of the obtained results.     

Oscillator Representation for Pseudoharmonic Potential

Oscillator representation method is applied to obtain the bound state energy eigenvalues and the corresponding eigenfunctions of the n-dimensional Schrödinger equation for the pseudoharmonic potential with arbitrary angular momentum.     

Der Drehimpulssatz in der Thermodynamik der irreversiblen Prozesse

The conservation law of the angular momentum has not been given sufficient attention in thermodynamics of irreversible processes. It plays an important part, however, when irreversible processes in the presence of electromagnetic fields are examined and the intrinsic angular momentum, due to spins of electrons and nuclei and electron orbits in atoms and molecules, is taken account of. Then the thermodynamic properties of matter with the macroscopic intrinsic angular momentum as an additional extensive parameter can be developed. Thermodynamics of irreversible processes is completed by the fact that a characteristic irreversible process is now associated also with the conservation law of angular momentum and Bloch's equation of nuclear induction is thus obtained in a straightforward way as one of the phenomenological equations.     

The motion of an isoscalar particle in a dyon field

The motion of an isoscalar particle in a non-abelian dyon field is solved. We get the energy levels and eigenfunctions. The compound system has half odd integer quantum number for its angular momentum. Related problems will be discussed in another paper.     

轨道角动量分量算符的本征函数间的变换

本文讨论了不同轨道角动量分量算符本征函数间的变换关系,给出了对应的变换系数的计算方法,求解了几个比较常见情形l=1,2,3的变换系数,得到了各个变换系数之间的规律.     

Solving Laguerre-Gauss Mode Eigenvectors and Eigenfunctions in Entangled State Representation

We solve the Laguerre-Gauss mode eigenvectors and eigenfunctions in the entangled state representation by searching for common eigenvectors of the 2-dimensional harmonic oscillator's total energy operator and the angular momentum operator. We find that in the entangled state representation the eigen-solution satisfies the Hukuhara equation, and its solution is confluent hypergeometric function.     

Non-Relativistic Treatment of a Generalized Inverse Quadratic Yukawa Potential

A bound state solution is a quantum state solution of a particle subjected to a potential such that the particle's energy is less than the potential at both negative and positive infinity. The particle's energy may also be negative as the potential approaches zero at infinity. It is characterized by the discretized eigenvalues and eigenfunctions,which contain all the necessary information regarding the quantum systems under consideration. The bound state problems need to be extended using a more precise method and approximation scheme. This study focuses on the non-relativistic bound state solutions to the generalized inverse quadratic Yukawa potential. The expression for the non-relativistic energy eigenvalues and radial eigenfunctions are derived using proper quantization rule and formula method, respectively. The results reveal that both the ground and first excited energy eigenvalues depend largely on the angular momentum numbers, screening parameters, reduced mass, and the potential depth. The energy eigenvalues,angular momentum numbers,screening parameters,reduced mass,and the potential depth or potential coupling strength determine the nature of bound state of quantum particles. The explored model is also suitable for explaining both the bound and continuum states of quantum systems.     

A neutral spinning particle in interaction with a magnetic field and Poschl–Teller potential

The problem of a neutral spinning particle in interaction with a linear increasing rotating magnetic field and a Poschl–Teller potential is considered via path integrals. The calculations are carried out explicitly using an external current source. The problem is then reduced to that of a spinning forced Poschl–Teller oscillator whose spin is coupled to external derivative current sources. The result of the propagator is given as a series. The relative propagator of this forced oscillator is converted to that of an angular momentum via an extension of the dimension. Next, the series is exactly summed by means of a Laplace transformation and the orthonormalization relation of the eigenfunctions of the angular momentum. Received: 29 June 2001 / Published online: 23 November 2001     

A class of exactly solvable potentials II. The three-dimensional Schrödinger equation

The three-dimensional Schrödinger equation with an effective mass is solved for a new class of angular momentum dependent potentials with varying depths and shapes. The energy eigen, values and resonances are given in algebraic form as a function of the effective mass and depth and shape of the potential. The eigenfunctions, scattering function, and Green's function are given in closed form in terms of known special functions. The charge density of ²⁰⁸Pb is calculated using eigenfunctions of a particular potential and this charge density is compared to the measured charge density.     

On the Aharonov–Bohm Hamiltonian

Using the theory of self-adjoint extensions, we construct all the possible Hamiltonians describing the nonrelativistic Aharonov–Bohm effect. In general, the resulting Hamiltonians are not rotationally invariant so that the angular momentum is not a constant of motion. Using an explicit formula for the resolvent, we describe the spectrum and compute the generalized eigenfunctions and the scattering amplitude.     

量子环上粒子体系的计算

对于量子环上带电粒子体系,组成本征函数的基矢数及哈密顿矩阵元素数都极大,数值计算量庞大.本文介绍在处理此问题时按轨道总角动量分类从基矢集中选择子基矢集的方法和技巧.应用计算机进行数值计算时,此方法比以往节省90%以上的时间.     

三维各向同性谐振子的代数解法

用带角动量的玻色算子统一构成三维各向同性谐振子的能量本征函数，并讨论了它们和直接求解微分方程得到的本征解之间的关系．这种方法快捷优美，而且有统一的表达式和简单的李代数关系。     

Transformation Between Eigenfunctions of Three Components of Geometric Momentum on Two-Dimensional Sphere

A technique of coordinate transformation is devised to overcome the computational difficulty associated with the direct transformation between eigenfunctions of three components of the geometric momentum on two-dimensional spherical surface, and the computations are firstly carried out in new coordinates and secondly the results are transformed back into the original coordinates. The eigenfunctions of different components of geometric momentum is explicitly demonstrated to transform under the spatial rotations in the precise way we anticipate.     

Transformation Between Eigenfunctions of Three Components of Geometric Momentum on Two-Dimensional Sphere

A technique of coordinate transformation is devised to overcome the computational difficulty associated with the direct transformation between eigenfunctions of three components of the geometric momentum on two-dimensional spherical surface, and the computations are firstly carried out in new coordinates and secondly the results are transformed back into the original coordinates. The eigenfunctions of different components of geometric momentum is explicitly demonstrated to transform under the spatial rotations in the precise way we anticipate.     

On the exact solution of the harmonic quadrupole collective hamiltonian

Explicit expressions for the eigenfunctions of the harmonic quadrupole collective Hamiltonian both in the lab and intrinsic systems of references are given. Two alternative approaches, the technique of projective coherent states and the theory of harmonic polynomials in collective coordinates, are used. Symmetry properties and recursive formulae for the internally labelled wave functions are established. Applications to the yrast states as well as to the low angular momentum states in the case of the asymmetric rotor Hamiltonian are also presented.     

Strong Jahn-Teller coupling of ionic Eg orbitals to a cluster in the harmonic approximation

A study is made of two useful perturbation schemes describing theE _g orbitals of a paramagnetic ion coupled very strongly to a cluster surrounding a cubically symmetric lattice site in the harmonic approximation. The two methods correspond to the cases when the vibrational states have low and large angular momentum. The limitations of both approaches are discussed and the zero order eigenvalues and eigenfunctions are given in each case.     

Arbitrary <Emphasis Type="Italic">l</Emphasis>-state solutions of the Schrödinger equation for the Eckart potential with an improved approximation of the centrifugal term

Applying an improved approximation scheme to the centrifugal term, the approximate analytical solutions of the Schrödinger equation for the Eckart potential are presented. Bound state energy eigenvalues and the corresponding eigenfunctions are obtained in closed forms for the arbitrary radial and angular momentum quantum numbers, and different values of the screening parameter. The results are compared with those obtained by the other approximate and numerical methods. It is shown that the present method is systematic, more efficient and accurate.