The hydrino and other unlikely states

We discuss the tightly bound (hydrino) solution of the Klein–Gordon equation for the Coulomb potential in 3 dimensions. We show that a similar tightly bound state occurs for the Dirac equation for the Coulomb potential in 2 dimensions. These states are unphysical since they disappear if the nuclear charge distribution is taken to have an arbitrarily small but non-zero radius.     

具有P?schl-Teller型标量势与矢量势的Klein-Gordon方程和Dirac方程的束缚态

给出了具P?schl-Teller型标量势与矢量势的Klein-Gordon方程和Dirac方程的s波束缚态解. 关键词： P?schl-Teller势 Klein-Gordon方程 Dirac方程 束缚态     

The spin symmetry for deformed generalized Pöschl-Teller potential

In the case of spin symmetry we solve the Dirac equation with scalar and vector deformed generalized Pöschl-Teller (DGPT) potential and obtain exact energy equation and spinor wave functions for s-wave bound states. We find that there are only positive energy states for bound states in the case of spin symmetry based on the strong regularity restriction condition λ<−η for the wave functions. The energy eigenvalue approaches a constant when the potential parameter α goes to zero. Two special cases such as generalized PT potential and standard PT potential are also briefly discussed.     

A Microscopic Calculation of Nucleon-Antinucleon Bound States

A microscopic study of nucleon-antinucleon (N N) bound states is achieved starting from the relativistic Pauli-Schrödinger equation for q³q³ bound states. From this equation, a complex off-shell qq one-gluon-exchange potential is derived. Use of this potential and the resonating group method to calculate the NN bound states leads to results which are useful to analyze some of the NN experimental data reported in recent years.     

A Schrödinger Potential Conditionally Integrable in Terms of the Hermite Functions

We introduce a biconfluent Heun potential well for the one-dimensional stationary Schrödinger equation which is composed of a confining fraction-power term and a repulsive centrifugal-barrier core. This is a conditionally integrable potential in that the strength of the centrifugal barrier is fixed to a constant. The potential supports a countable infinite number of bound states. We present the general solution of the Schrödinger equation, deduce the exact equation for the energy spectrumand derive a highly accurate approximation for energy levels. The bound state wave functions are written as irreducible linear combinations with constant coefficients of two Hermite functions of a scaled and shifted argument.

     

具有Kratzer型标量势与矢量势的Klein-Gordon方程和Dirac方程的束缚态

给出了具有Kratzer型标量势与矢量势的Klein-Gordon方程和Dirac方程的s波束缚态解.     

Bound states resulting from interaction of the non-relativistic particles with the multiparameter potential

In this study, we present the analytical solutions of bound states for the Schrodinger equation with the multiparameter potential containing the different types of physical potentials via the asymptotic iteration method by applying the Pekeristype approximation to the centrifugal potential. For any n and l(states) quantum numbers, we derive the relation that gives the energy eigenvalues for the bound states numerically and the corresponding normalized eigenfunctions. We also plot some graphics in order to investigate effects of the multiparameter potential parameters on the energy eigenvalues.Furthermore, we compare our results with the ones obtained in previous works and it is seen that our numerical results are in good agreement with the literature.     

氘-氘两体紧束缚态模型

提出了氘－氘紧束缚态模型．对两个氘原子核组成的体系,采用库仑势垒与核力方势阱组合的相互作用势,求解定态薛定谔方程,得到了两体紧束缚态的波函数和可能的能量本征值（核的库仑能数量级）,并说明了这种紧束缚态的存在条件． Deuterion deuterion tight bound states model about the mechanism of so called “nuclear cold fusion” is proposed. To solve the stationary Schrodinger equation with combination potential which contains Coulomb barrier and square well potential from nuclear force for the system containing two deuterions, the wave functions, the energy eigenvalues of the probable tight bound states and the existence condition of the tight bound states are obtained. In the case of ground...     

Effective Mass and Pseudoscalar Interaction in the Dirac Equation with Woods–Saxon Potential

We consider the one-dimensional Dirac equation with the Woods–Saxon potential in the Framework of position dependent mass and pseudoscalar interaction. By imposing appropriate constraints on the mass function and the pseudoscalar term new exact solvable models are obtained. A detailed study of the scattering and bound-states problems for these models is presented. Meanwhile, we work out the exact expressions for the transmission and reflection probabilities of scattered states and obtain the exact equation for the energy eigenvalues associated to bound states. In particular, transmission resonance at zero-momentum is observed for supercritical states.     

Scattering and bound states of spinless particles in a mixed vector–scalar smooth step potential

Scattering and bound states for a spinless particle in the background of a kink-like smooth step potential, added with a scalar uniform background, are considered with a general mixing of vector and scalar Lorentz structures. The problem is mapped into the Schrödinger-like equation with an effective Rosen–Morse potential. It is shown that the scalar uniform background present subtle and trick effects for the scattering states and reveals itself a high-handed element for formation of bound states. In that process, it is shown that the problem of solving a differential equation for the eigenenergies is transmuted into the simpler and more efficient problem of solving an irrational algebraic equation.     

库仑势加新环形势的相对论束缚态

在标量势等于矢量势的条件下，获得了库仑势加新环形势的Klein-Gordon方程和Dirac方程的束缚态的精确解. 对于Klein-Gordon方程，获得了精确的能谱方程和归一化的波函数. 对于Dirac方程，给出了精确的能谱方程和归一化的旋量波函数. 关键词： 库仑势加新环形势 束缚态 精确解     

Quasibound states in semiconductor quantum well structures

We present a study on quasibound states in multiple quantum well structures using a finite element model (FEM). The FEM is implemented for solving the effective mass Schrödinger equation in arbitrary layered semiconductor nanostructures with an arbitrary applied potential. The model also includes nonparabolicity effects by using an energy dependent effective mass, where the resulting nonlinear eigenvalue problem was solved using an iterative approach. We focus on quasibound/continuum states above the barrier potential and show that such states can be determined using cyclic boundary conditions. This new method enables the determination of both bound and quasibound states simultaneously, making it more efficient than other methods where different boundary conditions have to be used in extracting the relevant states. Furthermore, the new method lifted the problem of quasibound state divergence commonly seen with many other methods of calculation. Hence enabling accurate determination of dipole matrix elements involving both bound and quasibound states. Such calculations are vital in the design of intersubband optoelectronic devices and reveal the interesting properties of quasibound states above the potential barriers.     

A study of the bound states for square potential wells with position-dependent mass

A potential well with position-dependent mass is studied for bound states. Applying appropriate matching conditions, a transcendental equation is derived for the energy eigenvalues. Numerical results are presented graphically and the variation of the energy of the bound states are calculated as a function of the well-width and mass.     

On the Asymptotic Stability of Bound States in 2D Cubic Schrödinger Equation

We consider the cubic nonlinear Schrödinger equation in two space dimensions with an attractive potential. We study the asymptotic stability of the nonlinear bound states, i.e. periodic in time localized in space solutions. Our result shows that all solutions with small, localized in space initial data, converge to the set of bound states. Therefore, the center manifold in this problem is a global attractor. The proof hinges on dispersive estimates that we obtain for the non-autonomous, non-Hamiltonian, linearized dynamics around the bound states.     

Raising and Lowering of Generalized Hulthén Potential from Supersymmetry Approaches

We obtain the exact bound states of the generalized of Hulthén potential with negative energy levels using an analytic approach. In order to obtain bound states, we use the associated Jacobi differential equation. Using the supersymmetry approach to quantum mechanics, we show that these bound states, via four pairs of first order differential operators, represent four types of ladder equations. Two types of these supersymmetric structures suggest derivation of algebric solutions for the bound states using two different approaches. PACS 21.60.Cs; 21.60.Fw; 21.60.-n; 03.65.Fd; 03.65.Ge; 03.65.-w     

Bi-Confluent Heun Potentials for a Stationary Relativistic Wave Equation for a Spinless Particle

The variety of bi-confluent Heun potentials for a stationary relativistic wave equation for a spinless particle is presented. The physical potentials and energy spectrum of this wave equation are related to those for a corresponding Schrödinger equation in the sense that all the potentials derived for the latter equation are also applicable for the wave equation under consideration. We show that in contrast to the Schrödinger equation the characteristic spatial length of the potential imposes a restriction on the energy spectrum that directly reflects the uncertainty principle. Studying the inversesquare- root bi-confluent Heun potential, it is shown that the uncertainty principle limits, from below, the principal quantum number for the bound states, i.e., physically feasible states have an infimum cut so that the ground state adopts a higher quantum number as compared to the Schrödinger case.     

赝自旋对称性条件下四参量双原子分子势中相对论粒子的束缚态

在赝自旋对称性条件下,严格求解了四参量双原子分子势中运动粒子的s波Klein-Gordon方程和Dirac方程,并给出了相应的束缚态能谱和相对论性波函数.     

keV量级光子的线辐射源

在天体空间或实验室的等离子体中可能存在能量为若干keV量级的光子的线辐射,它们源于一种新的原子核物质结构形态(核核两体的松聚合)形成之时.对两个原子核组成的体系,采用库仑势垒与核力方势阱相组合的作用势,求解核核两体的定态薛定谔方程,得到了两体松束缚态的波函数和可能的能量本征量(核的长程库仑能的数量级)并说明了这种松束缚态的存在条件.对某些轻核,基态的结合能为若干keV.     

Localization of a pair of bound particles in a random potential

We study the localization length l_c of a pair of two attractively bound particles moving in a one-dimensional random potential. We show in which way it depends on the interaction potential between the constituents of this composite particle. For a pair with many bound states N the localization length is proportional to N, independently of the form of the two particle interaction. For the case of two bound states, we present an exact solution for the corresponding Fokker–Planck equation and demonstrate that l_c depends sensitively on the shape of the interaction potential and the symmetry of the bound state wave functions.