反向量子势重构 via 通用伯特兰-马丁不等式
Inverse Quantum Potential Reconstruction via Generalized Bertlmann-Martin Inequalities
AI总结：
通过通用伯特兰-马丁不等式构建拉普拉斯-动量重构流程，利用伯特兰-马丁间隙界与广义伯特兰-马丁偶动量阶梯连接，结合帕德近似和反变换恢复ρ(r)和V(r)，并用物理一致的插值方案补充奇动量。
摘要：
从几个束缚态能级重构径向(一维)量子势V(r)是一个长期存在的反问题，因为有限的谱数据必须约束整个势。我们提出了一种拉普拉斯-动量重构流程，将伯特兰-马丁间隙界与广义伯特兰-马丁(GBM)偶动量阶梯连接，继续用帕德近似扩展拉普拉斯变换，并反向变换以恢复ρ(r)和V(r)。奇动量通过物理一致的插值方案提供。对库仑、谐振子、胡尔滕、克拉特泽和双曲井情况的基准设置和诊断被陈述，以便每个近似阶段可以在共同的经验基础上评估。结论因此仅限于报告的基准设置，而不是作为普遍方法声明。
英文摘要：
Reconstructing a radial (1D) quantum potential, V(r), from a few bound-state energies is a long-standing inverse problem because limited spectral data must constrain an entire potential. We present a Laplace-moment reconstruction pipeline that links the Bertlmann-Martin gap bound to generalized Bertlmann-Martin (GBM) even-moment ladders, continues the Laplace transform with Pade approximants, and inverts the transform to recover rho(r) and V(r). Odd moments are supplied by a physically consistent interpolation scheme. Benchmark settings and diagnostics for Coulomb, harmonic oscillator, Hulthen, Kratzer, and hyperbolic-well cases are stated so each approximation stage can be assessed under a common empirical basis. The conclusions are therefore limited to the reported benchmark settings rather than offered as universal method claims.
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