Hulthén势任意l波束缚态的近似解析解

在任意l波的离心项1/r2用δ2e-δr/(1-e-δr)2近似表达的条件下,对Hulthen势的径向Schrodinger方程作自变量指数变换,使此转化为超几何微分方程,获得了Hulthen势任意l波束缚态的解析解.给出了解析的能谱方程和用超几何多项式表示的归一化的径向波函数,讨论了近似解析解的意义.     

On the approximate solution through continued fractions of the schrödinger equation with central potentials for positive energies

We present an extension to positive energies of an approximation method based on continued fractions already used to provide approximate energies and wave functions for bound states. A formalism particularly adapted for numerical computation is proposed and its applications are shown for the free particle case and short and long range central potentials, for the lowest angular momenta. The domain of convergence is displayed; especially for low and medium energies, the results are quite good. Some care is devoted to the successful determination of theS-wave scattering length for the Yukawa potential. The mathematical relationship with Calogero's formulation of the problem is established.     

Stieltjes electrostatic model interpretation for bound state problems

In this paper, it is shown that Stieltjes electrostatic model and quantum Hamilton Jacobi formalism are analogous to each other. This analogy allows the bound state problem to mimic as n unit moving imaginary charges \(i\hbar \) , which are placed in between the two fixed imaginary charges arising due to the classical turning points of the potential. The interaction potential between n unit moving imaginary charges \(i\hbar \) is given by the logarithm of the wave function. For an exactly solvable potential, this system attains stable equilibrium position at the zeros of the orthogonal polynomials depending upon the interval of the classical turning points.     

Application of the hyperspherical formalism to the trinucleon bound state problems

A method for solving the Schrödinger equation for the ground state of any number of bosons or for the trinucleon system or α-particle is formulated in the framework of the hyperspherical harmonic expansion method. It is applied to the trinucleon system for nucleons interacting through realistic soft core potentials. The convergence of the method is carefully studied. Binding energies, electric form factors, one body densities, two body correlation functions and two body photodisintegration are calculated for various potentials.     

A rigorous foundation of an easy-to-apply approximation method for bound state problems

Recently the application of a non-expensive scattering theory method to bound state problems has been proposed on the grounds of intuitive arguments. Subsequent realistic calculations have manifested advantageous features of the method especially in problems in which the asymptotic behaviour of the wave function is important. Here it is rigorously proven that the method is convergent, and mathematically correct procedures are described that speed up convergence and make the approximate energies approach the exact value from one side only. The general considerations are visualized by numerical results of a model problem.     

The physical solution of the three magnon bound state equation in one dimension

A direct derivation of the physical eigenvalue and eigenfunction for the three magnon bound state equation is given.     

Scheidegger''s rivers, Takayasu''s aggregates and continued fractions

A discrete model of (1+1)-dimensional aggregation, equivalent to Scheidegger's 1967 river model, is tackled with continued fractions. An exact expression for the power-law distribution of aggregate masses is found.     

The jost function and bound state solution for the hulthén potential

The parameters of the attractive Hulthén potential are obtained in terms of the parameters of effective range theory by using the Jost function for the potential. The bound state solution for 1 + 0 is found from the corresponding Jost solution. The possibility of extending the present treatment to higher angular momentum states is discussed.     

The bound state solution for the Morse potential with a localized mass profile

We investigate an analytical solution for the Schr o¨dinger equation with a position-dependent mass distribution, with the Morse potential via Laplace transformations. We considered a mass function localized around the equilibrium position.The mass distribution depends on the energy spectrum of the state and the intrinsic parameters of the Morse potential. An exact bound state solution is obtained in the presence of this mass distribution.     

Hartmann势加新环型势的相对论束缚态解(英文)

在矢势与标势相等的情况下,对Hartmann势加新环型势的Klein-Gordon方程精确求解.给出了归一化的角向和径向波函数,同时获得了能谱方程.     

The positron-helium bound state

A variational calculation with a trial wave function including up to 17 parameters has been used to investigate the existence of a positron-helium bound state. The resulting binding energy was found to be greater than the helium binding energy, and thus it is believed that the positron does not get bound to a helium atom. The calculations provide also values of ground state helium energy and the corresponding wave functions.     

Second bound state of PsH

The existence of a second bound state of PsH that is electronically stable and also stable against positron annihilation by the normal 2gamma and 3gamma processes is demonstrated by explicit calculation. The state can be found in the ;{2,4}S;{o} symmetries with the two electrons in a spin-triplet state. The binding energy against dissociation into the H(2p)+Ps(2p) channel was 7.03 x 10;(-4) hartree. The dominant decay mode of the states will be radiative decay into a configuration that autoionizes or undergoes positron annihilation. The NaPs system of the same symmetry is also electronically stable with a binding energy of 1.514 x 10;(-3) hartree with respect to the Na(3p)+Ps(2p) channel.     

Approximate solution for kinetic differential equations

Summary In the present work we show the analysis of an approximate solution for the coupled kinetic differential equations of a defect involving processes of untrapping, retrapping and recombination annihilation, using the Poincaré-Dulac theorem. The authors of this paper have agreed to not receive the proofs for correction.