Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

理论物理通讯：英文版

A Particle Interacting with V-shaped Potential Decorated by a Dirac Delta Function Interaction at Center

王鑫, 唐量辉, 吴仍来, Wang Ya Nan, 刘全慧

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

Schr ? 为在一个排斥或漂亮的迪拉克三角洲功能相互作用在中心装饰的塑造 V 的潜力的一个粒子的 dinger 方程被解决，没有装饰，在原来的系统的平同等值的状态上表明点相互作用的关键影响。作为吸引力增加的力量，没有限制，扎根的州的精力掉下来；并且在无穷地大的吸引力的限制，扎根的状态走近一个单个州。我们的分析和结论能乐意地被概括到任何一个维的系统一个粒子在中心加迪拉克三角洲函数相互作用与对称的潜力交往。

Related papers

Modified Dirac delta function and modified dirac delta potential in the quantum mechanics

Won Sang Chung, HASSAN HASSANABADI

The European Physical Journal Plus•Jan 1, 2022•2 citations

Scattering of position-dependent mass Schrödinger equation with delta potential

HASSAN HASSANABADI, Won Sang Chung, Soroush Zare +1 more

The European Physical Journal Plus•Mar 1, 2017•17 citations

A Particle Interacting with V-shaped Potential Decorated by a Dirac Delta Function Interaction at Center

Wang Xin, Tang Liang-Hui, Wu Reng-Lai +2 more

The Schrödinger equation for a particle in the V-shaped potential decorated by a repulsive or attractive Dirac delta function interaction at the center is solved, demonstrating the crucial influence of point interaction on the even-parity states of the original system without decoration. As strength of the attraction increases, the ground state energy falls down without limit; and in limit of infinitely large attraction, the ground state approaches a singular state. Our analysis and conclusion can be readily generalized to any one-dimensional system a particle interacts with symmetrical potential plus the Dirac delta function interaction at the center.

Communications in Theoretical Physics•Feb 1, 2010•5 citations

Bound States Solution of Dirac Equation and Schrdinger Equation for a New Ring Potential

HU Xian-quan

Under strong coupling conditions,the non-relativistic motion of particles and spin zero or half-integer the nature of relativistic particles in the system with the Schrdinger equation and Dirac equation can respectively describe.A new ring-shaped harmonic oscillator potential is proposed in this paper.The exact bound solution of Dirac equation and Schrdinger equation for the above potential is obtained under the condition of equal scalar potentials and vector potentials.They can be separated into an corresponding to the wave function equations of angular and radial wave function equation with the method of separation variables.The normalized angle wave function and radial wave function were expressed respectively in terms of the generalized associated-Legendre function and the confluent hyper-geometric function are presented,that the normalized radial wave function,and then by the radial bound state wave function are satisfied with the boundary conditions,obtains the exact bound state energy spectrum equations.The exact energy spectrum equations are obtained and meanwhile,proper discussion and some important conclusions are presented.

Chongqing Shifan Daxue xuebao. Ziran kexue ban•Jan 1, 2011•0 citations

Schrödinger equation for a dirac bubble potential

S. M. Blinder

Chemical Physics Letters•Jul 1, 1979•14 citations

Analytic Solution of the Schrdinger Equation in the Non-spherical Ring Shaped Oscillator

HU Xian-quan

Most of Schrdinger equations in quantum mechanics haven't analytic solutions except the problems of well with infinite depth,one-dimensional linear harmonic oscillator and Coulomb's potential as well as three-dimensional isotropic harmonic oscillator.These Schrdinger equations include the various equations in the non-spherical ring shaped oscillator potential that haven't analytic solutions. We can only solve these problems approximately in our research activities, but the solving process of these problems is often exceptional complex.The limitation handicaps us to lucubrate the idiographic problems.This paper adopts NU Method(A.F.Nikiforov-V.B.Uvarov Method) to solve the angular equation of the Schrdinger equation in the non-spherical ring shaped oscillator potential V(r,θ)=μω2r2/2+2α/(2μr2)+2βcosθ/(2μr2sin2θ).We decompose the Schrdinger equation in the non-spherical ring shaped oscillator potential step by step until we obtains the analytic solutions of the equation,thus we obtain the analytic solution of the angular eigenfunction,and simplify the process of solutions.Moreover,this paper adopts special functions in the radial equation at the same time to broaden our study in solving the Schrdinger equations.

Chongqing Shifan Daxue xuebao. Ziran kexue ban•Jan 1, 2008•0 citations
Schr ? 为在一个排斥或漂亮的迪拉克三角洲功能相互作用在中心装饰的塑造 V 的潜力的一个粒子的 dinger 方程被解决，没有装饰，在原来的系统的平同等值的状态上表明点相互作用的关键影响。作为吸引力增加的力量，没有限制，扎根的州的精力掉下来；并且在无穷地大的吸引力的限制，扎根的状态走近一个单个州。我们的分析和结论能乐意地被概括到任何一个维的系统一个粒子在中心加迪拉克三角洲函数相互作用与对称的潜力交往。
The Schrödinger equation for a particle in the V-shaped potential decorated by a repulsive or attractive Dirac delta function interaction at the center is solved, demonstrating the crucial influence of point interaction on the even-parity states of the original system without decoration. As strength of the attraction increases, the ground state energy falls down without limit; and in limit of infinitely large attraction, the ground state approaches a singular state. Our analysis and conclusion can be readily generalized to any one-dimensional system a particle interacts with symmetrical potential plus the Dirac delta function interaction at the center.
Under strong coupling conditions,the non-relativistic motion of particles and spin zero or half-integer the nature of relativistic particles in the system with the Schrdinger equation and Dirac equation can respectively describe.A new ring-shaped harmonic oscillator potential is proposed in this paper.The exact bound solution of Dirac equation and Schrdinger equation for the above potential is obtained under the condition of equal scalar potentials and vector potentials.They can be separated into an corresponding to the wave function equations of angular and radial wave function equation with the method of separation variables.The normalized angle wave function and radial wave function were expressed respectively in terms of the generalized associated-Legendre function and the confluent hyper-geometric function are presented,that the normalized radial wave function,and then by the radial bound state wave function are satisfied with the boundary conditions,obtains the exact bound state energy spectrum equations.The exact energy spectrum equations are obtained and meanwhile,proper discussion and some important conclusions are presented.
Most of Schrdinger equations in quantum mechanics haven't analytic solutions except the problems of well with infinite depth,one-dimensional linear harmonic oscillator and Coulomb's potential as well as three-dimensional isotropic harmonic oscillator.These Schrdinger equations include the various equations in the non-spherical ring shaped oscillator potential that haven't analytic solutions. We can only solve these problems approximately in our research activities, but the solving process of these problems is often exceptional complex.The limitation handicaps us to lucubrate the idiographic problems.This paper adopts NU Method(A.F.Nikiforov-V.B.Uvarov Method) to solve the angular equation of the Schrdinger equation in the non-spherical ring shaped oscillator potential V(r,θ)=μω2r2/2+2α/(2μr2)+2βcosθ/(2μr2sin2θ).We decompose the Schrdinger equation in the non-spherical ring shaped oscillator potential step by step until we obtains the analytic solutions of the equation,thus we obtain the analytic solution of the angular eigenfunction,and simplify the process of solutions.Moreover,this paper adopts special functions in the radial equation at the same time to broaden our study in solving the Schrdinger equations.