双曲型势的束缚态谱研究
Studies on the bound-state spectrum of hyperbolic potential
摘要：
利用广义伪谱方法研究了双曲势的束缚态。通过求解相关的非相对论性薛定谔方程，允许非均匀的、最佳的空间离散，有效地获得了任意$n, \ell$量子态的本征值和本征函数。精确到小数点后十位的本征值报告了大范围的潜在参数，从而涵盖了广泛的相互作用。在所有情况下都观察到与现有文献结果的良好一致性。对较高的州给予特别注意。给出了一些新的状态。第一次相当详细地研究了能量变化与潜在参数的关系。
英文摘要：
Bound states of hyperbolic potential is investigated by means of a generalized pseudospectral method. Significantly improved eigenvalues, eigenfunctions are obtained efficiently for arbitrary $n, \ell$ quantum states by solving the relevant non-relativistic Schrödinger equation allowing a non-uniform, optimal spatial discretization. Eigenvalues accurate up to tenth decimal place are reported for a large range of potential parameters; thus covering a wide range of interaction. Excellent agreement with available literature results is observed in all occasions. Special attention is paid for higher states. Some new states are given. Energy variations with respect to parameters in the potential are studied in considerable detail for the first time.
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