共查询到17条相似文献,搜索用时 109 毫秒
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提出了一种新的精确可解的三维解析势函数,即环形非球谐振子。势函数为V(γ,θ)=1/2mω^2γ^2 h^2/2mA/γ^2 h^2/2mb/γ^2sin^2θ。将环形非球谐振子势的Schroedinger方程在球坐标系中进行变量分离,得到了角向方程和径向方程,给出了精确的能谱方程,获得了用普遍的associated-Legendre多项式表示的归一化的角向波函数和用合流超几何函数表示的归一化的径向波函数。球谐振子、非球谐振子和环形振子的有关结果均作为特例包含在本文的一般结论之中。 相似文献
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非球谐振子势的精确解 总被引:6,自引:0,他引:6
严格求解了三维非球谐振,势的Schrodinger方程给出了精确的能谱方程和归一化的径向波函数.获得了径向幂次算符rs的矩阵元和平均值的计算公式及其递推关系. 相似文献
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获得了球谐振子径向算符r2s正偶次幂和负偶次幂平均值之间的一个递推关系,在-4s4情况下给出了平均值<nrl|r2s|nrl>的解析计算结果. 相似文献
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求解了非球谐振子势场中1/2自旋粒子满足的Dirac方程,Dirac哈密顿量包含有标量非球谐振子势S(r)和矢量非球谐振子势V(r).在Σ(r)=S(r)+V(r)=0和Δ(r)=V(r)-S(r)=0的条件下,解析地得到了Dirac旋量波函数的束缚态解和能谱方程,结果表明非球谐振子势
关键词:
非球谐振子势
Dirac方程
赝自旋对称性
束缚态 相似文献
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各向同性谐振子是量子理论中能够严格求解的可解势场之一.对它的研究和讨论,在理论上和实际的应用中都有重要意义.本文推导出了N维(N≥2)各向同性谐振子径向矩阵元〈nrl|rk|nr′l′〉的递推公式,在此基础上得到了平均值的递推公式,并且讨论了维各向同性谐振子径向矩阵元的递推公式的一般性,而文献[3]与[4]所给出的各向同性谐振子径向矩阵元的递推公式只是本文结论的特例. 相似文献
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In this paper a new ring-shaped harmonic oscillator for spin 1/2 particles is studied, and the corresponding eigenfunctions and eigenenergies are obtained by solving the Dirac equation with equal mixture of vector and scalar potentials. Several particular cases such as the ring-shaped non-spherical harmonic oscillator, the ring-shaped harmonic oscillator, non-spherical harmonic oscillator, and spherical harmonic oscillator are also discussed. 相似文献
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提出了一种新的类Quesne环状球谐振子势,应用二分量方法求解1/2-自旋粒子满足的Dirac方程, Dirac哈密顿量由标量和矢量类Quesne环状球谐振子势构成.在Σ=S(r)+V(r)=0的条件下,得到了Dirac旋量波函数下分量的束缚态解和能谱方程, 显示出类Quesne环状球谐振子势场中的赝自旋对称性.讨论了束缚态波函数和能谱方程的有关性质.
关键词:
类Quesne环状球谐振子势
Dirac方程
赝自旋对称性
束缚态 相似文献
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Min-Cang Zhang 《International Journal of Theoretical Physics》2009,48(9):2625-2632
The pseudospin symmetry for a ring-shaped non-spherical harmonic oscillator potential is investigated by solving the Dirac
equation with equal mixture of scalar and vector potentials with opposite signs. The normalized spinor wave function and energy
equation are obtained, the algebraic property of the energy equation and some particular cases are also discussed. 相似文献
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在球坐标系中研究了一类具有运动边界与含时频率的环状非球谐振子模型势的Schrdinger方程.应用坐标变换将运动边界转化为固定边界,从而获得了系统的精确波函数.研究表明,系统的角向波函数是一个推广的缔合勒让德多项式,径向波函数可以表示为贝赛耳函数.最后我们简单讨论了指数运动边界和指数含时频率这一特殊情况. 相似文献
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A new ring-shaped non-harmonic oscillator potential is proposed. The precise bound solution of Dirac equation with the potential is gained when the scalar potential is equal to the vector potential. The angular equation and radial equation are obtained through the variable separation method. The results indicate that the normalized angle wave function can be expressed with the generalized associated-Legendre polynomial, and the normalized radial wave function can be expressed with confluent hypergeometric function. And then the precise energy spectrum equations are obtained. The ground state and several low excited states of the system are solved. And those results are compared with the non-relativistic effect energy level in Phys. Lett. A 340 (2005) 94. The positive energy states of system are discussed and the conclusions are made properly. 相似文献
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Bound states of Klein—Gordon equation for double ring-shaped oscillator scalar and vector potentials 总被引:1,自引:0,他引:1 下载免费PDF全文
In spherical polar coordinates, double ring-shaped oscillator potentials have supersymmetry and shape invariance for θ and r coordinates. Exact bound state solutions of Klein—Gordon equation with equal double ring-shaped oscillator scalar and vector potentials are obtained. The normalized angular wavefunction expressed in terms of Jacobi polynomials and the normalized radial wavefunction expressed in terms of the Laguerre polynomials are presented. Energy spectrum equations are obtained. 相似文献
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Exact solutions of the Klein—Gordon equation with ring-shaped oscillator potential by using the Laplace integral transform 下载免费PDF全文
Sami Ortakaya 《中国物理 B》2012,21(7):70303-070303
We present exact solutions for the Klein-Gordon equation with a ring-shaped oscillator potential. The energy eigenvalues and the normalized wave functions are obtained for a particle in the presence of non-central oscillator potential. The angular functions are expressed in terms of the hypergeometric functions. The radial eigenfunctions have been obtained by using the Laplace integral transform. By means of the Laplace transform method, which is efficient and simple, the radial Klein-Gordon equation is reduced to a first-order differential equation. 相似文献