The Infinite Square Well with a Singular Perturbation

We study the influence of a singular potential on an infinite square well. Two cases are considered. In the first, the singular potential is centered in the potential well, in the second case it is off-center. We also present a discussion on the self adjointness of the Hamiltonian of some exactly solvable potentials perturbed with singular potentials.     

Squeezing Dynamics for One-Dimensional Infinite Square Well with a Mobile Wall

We show that the dynamics for a particle confined in one-dimensional infinite square well with a mobile boundary can be converted to the case as if the boundary is time-independent at the expense of an appropriate time-dependent Hamiltonian. The Hamiltonian is deduced by the technique of integration within an ordered product of operators.     

The Coherence Time of Infinite Quantum Well

The relationship among the Coherence time (CT) τ, the Variation frequency λ, the energy separation ΔE and coupling constant α in quantum well was investigated using Pekar type variational method. The results indicated that the Coherence time τ is positively proportional to the Variation frequency λ, but the energy separation ΔE and coupling constant α are negatively correlated with the Coherence time τ. When ΔE is more than 10ev, and when α is more than 5, τ decreases sharply.     

无限深量子阱中强耦合极化子的基态结合能

研究了无限深量子阱中极化子的基态性质,采用线性组合算符和变分相结合的方法导出了强耦合极化子的振动频率λ、基态能量E₀和基态结合能E_b,讨论了阱宽L和电子-LO声子耦合强度α对强耦合极化子的振动频率λ、基态能量E₀和基态结合能E_b的影响。通过数值计算,结果表明:强耦合极化子的振动频率和基态结合能随阱宽L的增大而减小,随电子-LO声子耦合强度α的增强而增大;基态能量随阱宽L的增大而减小,其绝对值随电子-LO声子耦合强度α的增强而增大;当量子阱阱宽L趋近于无限大和无限小两种极限情况下,分别与三维和二维极化子的结果相一致。     

正切平方量子阱中三次谐波产生的研究

用量子力学中的密度矩阵算符理论推导出了正切平方量子阱中三次谐波产生的解析表达式,并以典型的GaAs正切平方量子阱为例进行数值计算.计算结果表明,该势阱中的三次谐波系数与势阱深度y0、势阱宽度b和弛豫常数(Π)Γ有关.通过调节V0、b和(Π)Γ可以获得比较大的三次谐波系数,从而为实验研究和实际生产提供必要的理论依据.     

Gauge Symmetry and Transverse Symmetry Transformations in Gauge Theories

The transverse symmetry transformations associated with the normal symmetry transformations are proposed to build the transverse constraints on the basic vertices in gauge theories. I show that, while the BRST symmetry in non-Abelian gauge theory QCD (Quantum Chromodynamics) leads to the Slavnov-Taylor identity for the quark-gluon vertex which constrains the longitudinal part of thevertex, the transverse symmetry transformation associated with the BRST symmetry enables to derive the transverse Slavnov-Taylor identity for the quark-gluon vertex, which constrains the transverse part of the quark-gluon vertex from the gauge symmetry of QCD.     

On the Definition of Gauge Transformations in Gauge Theory

The different types of gauge transformations in gauge theory are discerned and defined in fiber bundle terms. The gauge gravitation case is analysed in order to examine various versions of the gauge gravitation theory.     

Gauge Symmetry and Transverse Symmetry Transformations in Gauge Theories

The transverse symmetry transformations associated with the normal symmetry transformations are proposed to build the transverse constraints on the basic vertices in gauge theories. I show that, while the BRST symmetry in non-Abelian gauge theory QCD （Quantum Chromodynamics） leads to the Slavnov-Taylor identity for the quark-gluon vertex which constrains the longitudinal part of the vertex, the transverse symmetry transformation associated with the BRST symmetry enables to derive the transverse Slavnov-Taylor identity for the quark-gluon vertex, which constrains the transverse part of the quark-gluon vertex from the gauge symmetry of QCD.     

The Infinite Square Well with a Point Interaction: A Discussion on the Different Parameterizations

The construction of Dirac delta type potentials has been achieved with the use of the theory of self adjoint extensions of non-self adjoint formally Hermitian (symmetric) operators. The application of this formalism to investigate the possible self adjoint extensions of the one dimensional kinematic operator $K=-\frac{d^{2}}{dx^{2}}$ on the infinite square well potential is quite illustrative and has been given elsewhere. This requires the definition and use of four independent real parameters, which relate the boundary values of the wave functions at the walls. By means of a different approach, that fixes matching conditions at the origin for the wave functions, it is possible to define a perturbation of the type aδ(x)+bδ′(x), thus depending on two parameters, on the infinite square well. The objective of this paper is to investigate whether these two approaches are compatible in the sense that perturbations like aδ(x)+bδ′(x) can be fixed and determined using the first approach.     

正切平方势阱中线性与非线性光学折射率变化的研究

利用正切平方势把电子的Schrodinger方程化为了超几何方程，并用超几何函数严格求解了电子的本征值和本征函数利用量子力学中的密度矩阵算符理论导出了正切平方势阱中的线性与三阶非线性光学折射率的解析表达式计算了该系统中的线性与非线性光学折射率变化的大小，讨论了影响折射率变化因素文章以典型的GaAs/AlGaAs势阱为例作了数值计算,数值计算结果表明，势阱的形状和入射光强对光学折射率的变化有着重要的影响.     

A Particle in a Magnetic Field of an Infinite Rectilinear Current

We consider the Schrödinger operator H=(i+A)² in the space L ₂(R ³) with a magnetic potential A created by an infinite rectilinear current. We show that the operator H is absolutely continuous, its spectrum has infinite multiplicity and coincides with the positive half-axis. Then we find the large-time behavior of solutions exp(–i H t)f of the time dependent Schrödinger equation. Our main observation is that a quantum particle has always a preferable (depending on its charge) direction of propagation along the current. Similar result is true in classical mechanics.     

Action Principle and Algebraic Approach to Gauge Transformations in Gauge Theories

The action principle is used to derive, by an entirely algebraic approach, gauge transformations of the full vacuum-to-vacuum transition amplitude (generating functional) from the Coulomb gauge to arbitrary covariant gauges and in turn to the celebrated Fock–Schwinger (FS) gauge for the Abelian (QED) gauge theory without recourse to path integrals or to commutation rules and without making use of delta functionals. The interest in the FS gauge, in particular, is that it leads to Faddeev–Popov ghosts-free non-Abelian gauge theories. This method is expected to be applicable to non-Abelian gauge theories including supersymmetric ones.     

A Polaron in a Quantum Dot Quantum Well

The polaron effect in a quantum dot quantum well (QDQW)system is investigated by using the perturbation method. Both the bound electron states outside and inside the shell well are taken into account . Numerical calculation on the CdS/HgS QDQW shows that the phonon correction to the electron ground state energy is quite significant and cannot be neglected.     

Quantum Nondemolition Measurements of a Particle in an Inhomogeneous Gravitational Field

In this work we obtain a family of quantum nondemolition variables for the case of a particle moving in an inhomogeneous gravitational field. Afterwards, we calculate the corresponding propagator, and deduce the probabilities associated with the possible measurement outputs. The comparison, with the case in which the position is being monitored, will allow us to find the differences with respect to the case of a quantum demolition measuring process.     

A Gauge Model for Quantum Mechanics on a Stratified Space

In the Hamiltonian approach on a single spatial plaquette, we construct a quantum (lattice) gauge theory which incorporates the classical singularities. The reduced phase space is a stratified Kähler space, and we make explicit the requisite singular holomorphic quantization procedure on this space. On the quantum level, this procedure yields a costratified Hilbert space, that is, a Hilbert space together with a system which consists of the subspaces associated with the strata of the reduced phase space and of the corresponding orthoprojectors. The costratified Hilbert space structure reflects the stratification of the reduced phase space. For the special case where the structure group is SU(2), we discuss the tunneling probabilities between the strata, determine the energy eigenstates and study the corresponding expectation values of the orthoprojectors onto the subspaces associated with the strata in the strong and weak coupling approximations.     

Nonlocality in the Expanding Infinite Well

According to D. Bohm's interpretation of quantum mechanics, a particle always has a well-defined spatial trajectory. A change in boundary conditions can nonlocally change that trajectory. In this note we point out a striking instance of this phenomenon that is easy to understand qualitatively.     

Dust Particle Properties in a Dual-Frequency Driven Sheath

We study characteristics of a single dust particle in a duai-frequency capacitively coupled plasma sheath, such as charging and suspending processes, using a collisionless self-consistent model. Also, the movement of the dust grain with time is investigated for the various radii and initial velocities. The numerical results show that, after several microseconds, the charging process of the dust particle reaches equilibrium, and the grain obtains its equilibrium position, In addition, it is found that the parameters of the low-frequency source impact on the charging and suspending processes of the dust grain significantly.