环状非有心球谐振子势场赝自旋对称性的三对角化表示

张民仓

陕西师范大学物理学与信息技术学院,西安,710062

通讯作者: 张民仓

Pseudospin symmetry for a noncentral electric dipole ring-shaped potential in the tridiagonal representation

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摘要: 提出一个包含非有心电耦极矩势的环状谐振子模型，在能够负载波动算子三对角化矩阵表示的完全平方可积L2空间讨论了这一势场的赝自旋对称性．利用三对角化矩阵方案，给出了波函数角向分量和径向分量展开系数满足的三项递推关系式．角向波函数和径向波函数分别以Jacobi多项式和Laguerre多项式表示，由径向分量展开系数递推关系式的对角化条件得到束缚态的能量谱．并以Descartes多项式的符号法则讨论了能量方程的代数结构．

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Abstract: A noncentral harmonic oscillatory ring-shaped potential is proposed, in which the noncentral electric dipole is included. The pseudospin symmetry for this potential is investigated by working in a complete square integrable basis that supports a tridiagonal matrix representation of the wave operator. The resulting three-term recursion relations for the expansion coefficients of the wavefunctions (both angular and radial) are presented. The angular/radial wavefunction is written in terms of the JacobiFLaguerre polynomials. The discrete spectrum of the bound state is obtained by diagonalizing the radial recursion relation. The algebraic property of energy equation is also discussed, showing the exact pseudospin symmetry

环状非有心球谐振子势场赝自旋对称性的三对角化表示

通讯作者: 张民仓

陕西师范大学物理学与信息技术学院,西安,710062

关键词:

Pseudospin symmetry for a noncentral electric dipole ring-shaped potential in the tridiagonal representation

Corresponding author:

陕西师范大学物理学与信息技术学院,西安,710062

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