二维耦合量子谐振子的本征值和本征函数

运用广义线性量子变换理论,给出一类二维耦合量子谐振子的能量本征值、本征函数、坐标和动量算符在能量表象中的矩阵元及演化算符.     

两个耦合谐振子体系能量本征值和本征函数的三种求解方法

本将以耦合项为ｍωｘ１ｘ２＋１／ｍｐ１ｐ２的两个谐振子体系为例，通过坐标、动量变换，占有数表象中的矩阵变换，占有数表象中的矩阵变换和幺正算符变换，给出了求解耦合体系能量本征值和本征函数的三种不同方法。这些方法可适用于各种耦合谐振子体系问题。     

正切平方势单量子阱的本征值和本征函数

鉴于“方形”势阱描述量子阱中的电子运动行为过于简单、过于理想,引入了正切平方势来代替,使结果得到了改善。在量子力学框架内,利用正切平方势把电子的Schrdinger方程化为超几何方程,利用系统参数和超几何函数严格地求解了电子的本征值和本征函数,并以Ga_1-xAl_xAs-GaAs-Ga_1-xAl_xAs量子阱为例计算了电子的能级和能级之间的跃迁。结果表明,电子在量子阱中的能量是量子化的,而相邻能级之间的跃迁给出与实验进一步符合的结果。     

正切平方势与平面沟道系统的本征值和本征函数

讨论和分析了常用的平面连续势，引入了新的正切平方势描写粒子-晶体相互作用.在量子力学框架内，把系统的本征值和本征函数问题化为超几何方程的本征值和本征函数问题.将 低位能级之间的自发辐射同实验进行了比较，结果表明理论和实验符合很好. 关键词： Schrdinger方程 超几何函数 沟道辐射 本征值 本征函数     

自旋结网圈表象中体积与面积本征值

利用抓算符作用的反称化和双元恒等式，通过计算，证明了3价和任意价自旋结网圈分别为体积和面积算符的本征态，并得到了体积本征值为2^-32l³₀∑ip_σp_τp_ρ和面积本征值为2^-1l²₀∑jp_l(j)的结果. 关键词： 体积算符 面积算符 本征值 自旋结网圈     

平面光波导本征值的精确解法及光场分析

提出了一种严格且精确的基于传播矩阵方法计算光波导的算法,可计算出光波导的本征值,并画出场分布曲线。本方法物理意义清晰,计算方便,适用于计算机编程,并可推广用于波长量级光器件的计算。     

开普勒径向方程的赝角动量解法及其归一化本征态和相干态

用赝角动量方法直接求解球坐标下束缚态开普勒径向方程. 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；同时给出相应的相干态. 关键词： 开普勒径向方程 赝角动量方法 本征值谱 本征函数 相干态     

七玻色模混和模型的本征态及本征值

利用参数 ，我们没有运用Bethe ansatz假设，直接求解了三种七玻色模混和模型的所有本征态和本征值。而此参数取决于一多项式的根，并且是可以在数字上严格求解的。     

求解格林函数的本征函数法

从本征函数理论出发，本文介绍了求解第一类格林函数的本征函数法。从而对格林函数的本征函数法建立进行一般的理论概括。最后举例说明应用。     

Collective state of electrons and impurities with a spin

The problem of states of an electron system interacting with impurities that have a spin of 1/2 is considered. It is shown that in the calculation of the energy of the system, the electron spin-flip processes and the formation of electron–hole–impurity flip spin (hole against the background of electrons with another spin projection) play the major role. Such complexes are accumulated in the system (a sort of Bose condensate of complexes is formed); this reduces the energy of the system, which is a linear function of the initial interaction of an electron with the impurity spin (in contrast, for example, to the result obtained in perturbation theory). The hole-type excitation and the spin excitation have a gap in the spectrum. Small parameters of the problem are the interaction of electrons with impurity spins and the number of impurities. The electron–electron interaction is not taken into account. Impurities are assumed to be distributed at random, and calculations are performed using the known averaging over the positions of impurities.     

SU(4) Fermi liquid state and spin filtering in a double quantum dot system

We study a symmetrical double quantum dot (DD) system with strong capacitive interdot coupling using renormalization group methods. The dots are attached to separate leads, and there can be a weak tunneling between them. In the regime where there is a single electron on the DD the low-energy behavior is characterized by an SU(4)-symmetric Fermi liquid theory with entangled spin and charge Kondo correlations and a phase shift pi/4. Application of an external magnetic field gives rise to a large magnetoconductance and a crossover to a purely charge Kondo state in the charge sector with SU(2) symmetry. In a four-lead setup we find perfectly spin-polarized transmission.     

Ground eigenvalue and eigenfunction of a spin-weighted spheroidal wave equation in low frequencies

Spin-weighted spheroidal wave functions play an important role in the study of the linear stability of rotating Kerr black holes and are studied by the perturbation method in supersymmetric quantum mechanics.Their analytic ground eigenvalues and eigenfunctions are obtained by means of a series in low frequency.The ground eigenvalue and eigenfunction for small complex frequencies are numerically determined.     

Skew scattering of electrons in a spin glass

The field and temperature dependences of the extraordinary Hall effect in alloys of the $\text{Au}$Fe system have been measured for the first time over a range that encompasses the spin glass regime. We are able to show how the data reflect the competition between the spin glass ordering interactions and the disruptive effects of temperature and applied magnetic field.     

Orbital and spin magnetism and dielectric response of electrons in metals

A survey is given of the theory of orbital and spin magnetism of electrons in metals, and of the relation of this to dielectric response theory. In particular, the orbital magnetic behaviour of Bloch electrons in a static but spatially varying magnetic field is discussed. It is shown that the treatment of Hebborn and Sondheimer can be generalized to include this spatial dependence of the applied magnetic field and that the result may be written compactly in terms of the zero field canonical density matrix, or Green function.

It is further shown that the frequency dependence of both the orbital and spin susceptibility can be obtained, again from the density matrix, by calculating the current. The connection with neutron scattering is exhibited and for the case of nickel the way in which such experiments can lead to estimates of the role of the electron interactions is discussed.

The effect of a magnetic field on phonon spectra in metals is considered briefly. Finally it is suggested that it may be of interest to study the effect of the magnetic field on the periodic potential usually employed to calculate energy levels of electrons in magnetic fields. Some modifications of pair forces between ions is to be expected in very high fields.     

The spin polarization of conduction electrons in ferromagnetic semiconductors

Within the framework of the s?f exchange model the exact asymptotics of the spin polarization of conduction electrons in the non-degenerate ferromagnetic semiconductor at low temperatures is calculated. It is demonstrated that the temperature dependent corrections to the total density of states are proportional to $\text{T}{}^{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$.     

Solving ground eigenvalue and eigenfunction of spheroidal wave equation at low frequency by supersymmetric quantum mechanics method

The spheroidal wave functions are found to have extensive applications in many branches of physics and mathematics. We use the perturbation method in supersymmetric quantum mechanics to obtain the analytic ground eigenvalue and the ground eigenfunction of the angular spheroidal wave equation at low frequency in a series form. Using this approach, the numerical determinations of the ground eigenvalue and the ground eigenfunction for small complex frequencies are also obtained.     

The study of magnetization of the spin system in the ground state

Within the framework of the effective-field theory with self-spin correlations and the differential operator technique, the ground state magnetizations of the biaxial crystal field spin system on the honeycomb lattices have been studied. The influences of the biaxial crystal field on the magnetization in the ground state have been investigated in detail.