双莫尔斯振子的位置与动量空间量子信息度量
Position- and Momentum-Space Quantum Information Measures of the Double-Morse Oscillator
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中文总结 AI 辅助
该研究计算双莫尔斯振子的量子信息度量，分析其位置与动量空间分布随参数A的变化规律，揭示基态与激发态费舍尔-香农乘积的不同特性。
中文摘要 AI 辅助
我们研究受双莫尔斯势约束的粒子在位置空间与动量空间中的量子信息性质。该模型的准精确可解性为前两个束缚态提供了解析表达式，使得可直接分析对应的概率密度。以参数 $A$ 的函数形式计算了香农熵、奥尼塞库能量、费舍尔信息、统计复杂性及费舍尔-香农乘积，参数 $A$ 控制着从分离良好的双势阱到合并单势阱轮廓的转变。当双势阱特征显著时，位置分布更离域且结构更复杂，而动量分布则呈现互补趋势。随着势阱合并，基态费舍尔-香农乘积趋近其高斯参考值，而激发态则保留更强的非高斯结构。
英文摘要
We investigate the quantum-information properties of a particle confined by the double Morse potential in position and momentum spaces. The quasi-exact solvability of the model gives analytical expressions for the first two bound states, allowing the corresponding probability densities to be analyzed directly. Shannon entropy, Onicescu energy, Fisher information, statistical complexity, and Fisher-Shannon products are evaluated as functions of the parameter $A$, which controls the transition from a well-separated double well to a merged single-well profile. The position distribution is more delocalized and structurally complex when the double-well character is pronounced, whereas the momentum distribution exhibits the complementary trend. As the wells merge, the ground-state Fisher--Shannon product approaches its Gaussian reference value, whereas the excited state retains stronger non-Gaussian structure.
