SOLITON SOLUTION OF NONLINEAR SCHRODINGER EQUATION WITH HIGHER ORDER DISPERSION TERMS

It is shown in this paper that if parameters β1,β2 and β3 of a nonlinear Schrodinger equation with higher order dispersion terms (HNLS) satisfy the condition: 6β1-β2-2β3(1- 6β1k)= 0, k a real constant, then the fundamental soliton solutions of the HNLS equation exist. The exact soliton solutions are given and the relation between this condition and the known results inthe literature is also discussed.     

Rigorous Solutions for the One-Dimensional Hartmann Potential in the Quantum Phase-Space Representation

The rigorous solutions of the Schrödinger equation with the one-dimensional Hartmann potential for a particle are solved and discussed within the framework of the quantum phase space representation established by Torres-Vega and Frederick. For a simple example, the uncertainty principle for the quantum probability density functions is revealed in phase space representation.     

Systems of orthogonal polynomials defined by hypergeometric type equations with application to quantum mechanics

A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated special functions and the corresponding raising/lowering operators. The equations considered are directly related to some Schrödinger type equations (Pöschl-Teller, Scarf, Morse, etc), and the special functions defined are related to the corresponding bound-state eigenfunctions.     

Harmonic oscillators in relativistic quantum mechanics

Relativistic generalisations of the harmonic oscillator are analysed. Lévy–Leblond, Dirac and Klein–Gordon equations which in the limit of a non-relativistic and spinless particle transform into Schrödinger equation for the harmonic oscillator are constructed. Properties of their solutions, in particular the structure of their spectra, are analysed. Applications to modelling phenomena relevant in quantum chemistry are briefly discussed.     

New Second-order Exponentially and Trigonometrically Fitted Symplectic Integrators for the Numerical Solution of the Time-independent Schrödinger Equation

The solution of the one-dimensional time-independent Schr?dinger equation is considered by trigonometrically and exponentially fitted symplectic integrators. The Schr?dinger equation is first transformed into a Hamiltonian canonical equation. Numerical results are obtained for the one-dimensional harmonic oscillator, doubly anharmonic oscillator and the exponential potential.     

On the single-electron local kinetic energy

Ｉｎｒｅｃｅｎｔｄｅｃａｄｅｓ,ｇｒｅａｔｐｒｏｇｒｅｓｓｈａｓｂｅｅｎｍａｄｅｉｎｔｈｅｄｅｎｓｉｔｙｆｕｎｃｔｉｏｎａｌｔｈｅｏｒｙａｎｄｉｔｓａｐｐｌｉｃａｔｉｏｎｓ.ＨｏｈｅｎｂｅｒｇＫｏｈｎｔｈｅｏｒｅｍｉｓｉｔｓｂａｓｉｓ.Ｔａｋｉｎｇｔｈｅｏｎｅｅｌｅｃｔｒｏｎｄｅｎｓｉｔｙａｓａｆｕｎｄａｍｅｎｔａｌｖａｒｉａｂｌｅ,ｔｈｉｓｔｈｅｏｒｙｔｒｅａｔｓｔｈｅｔｏｔａｌｅｎｅｒｇｙＥ[ρ]ｏｆｔｈｅｅｌｅｃｔｒｏｎｉｃｇｒｏｕｎｄｓｔａｔｅｆｏｒａｍｏｌｅｃｕｌｅａｓａｆｕｎｃｔｉｏｎａｌ…     

Precise potential harmonic approach to directly solving Schrödinger equations of helium-like three-body systems

A complete potential harmonic scheme is presented, including the linked coupled hyperradial ordinary differential equations and the secular equation of eigenenergy. It has been used to directly solve the Schrödinger equations of helium-like three-body systems (nuclear chargeZ = 1–9). and very accurate ground state eigenenergies as well as low-lying singlet excited state ones have been obtained.     

物理视角下的期权定价方程

以大学物理的角度来介绍三种推导Black—Scholes期权定价方程的方法，并以，物理专业易于理解的方式来剖析相关的推导过程．     

Spectral analysis of nonselfadjoint Schrödinger problem with eigenparameter in the boundary condition

In this paper we consider the nonselfadjoint (dissipative) Schrödinger boundary value problem in the limit-circle case with an eigenparameter in the boundary condition. Since the boundary conditions are nonselfadjoint, the approach is based on the use of the maximal dissipative operator, and the spectral analysis of this operator is adequate for the boundary value problem. We construct a selfadjoint dilation of the maximal dissipative operator and its incoming and outgoing spectral representations, which make it possible to determine the scattering matrix of the dilation. We construct a functional model of the maximal dissipative operator and define its characteristic function in terms of solutions of the corresponding Schrödinger equation. Theorems on the completeness of the system of eigenvectors and the associated vectors of the maximal dissipative operator and the Schrödinger boundary value problem are given.     

New Estimates for the Bottom of the Spectrum of Schrödinger Operators

We obtain a bound for the bottom of the negative spectrum of Schrödinger operators on weighted Riemannian manifolds in terms of F-Sobolev inequalities. Also, we show how an estimate for the first negative eigenvalue implies the F-Sobolev inequality.