谱中具有偶然简并的变曲率空间上的一族精确可解径向量子系统
A Family of Exactly Solvable Radial Quantum Systems on Space of Non-Constant Curvature with Accidental Degeneracy in the Spectrum
摘要：
提出了一类新的弯曲空间上的精确可解量子系统。该族是经典Perlick族的量子版本，它包括所有具有球对称性的最大超可积3维Hamilton系统。经典系统所表现出的大量对称性（几何和动力学）在量子系统的光谱中有一个对应的偶然简并。这一系列的量子问题是完全解决的技术的超对称量子力学。我们还详细分析了经典哈密顿量的动力学项的量子化中出现的排序问题，强调了两个物理意义的量子化之间存在的联系：几何量子化和位置相关的质量量子化。
英文摘要：
A novel family of exactly solvable quantum systems on curved space is presented. The family is the quantum version of the classical Perlick family, which comprises all maximally superintegrable 3-dimensional Hamiltonian systems with spherical symmetry. The high number of symmetries (both geometrical and dynamical) exhibited by the classical systems has a counterpart in the accidental degeneracy in the spectrum of the quantum systems. This family of quantum problem is completely solved with the techniques of the SUSYQM (supersymmetric quantum mechanics). We also analyze in detail the ordering problem arising in the quantization of the kinetic term of the classical Hamiltonian, stressing the link existing between two physically meaningful quantizations: the geometrical quantization and the position dependent mass quantization.
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