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arXiv 2512.22232quant-ph
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非相对论量子粒子在施特金-like势场下被限制在圆柱形表面的研究

Non-Relativistic Quantum Particle Confined on a Cylindrical Surface under a Stark-like Potential

National Tsing Hua University（国立清华大学）

Deriyan Senjaya

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AI总结：

本研究通过施特金-like势场对限制在圆柱形表面的量子粒子进行扰动，揭示隐藏维度的可能方法。

摘要：

本研究探讨了施特金-like扰动势对限制在圆柱形表面（QPCS）的量子粒子的影响及其对额外维度理论的意义。QPCS框架尤其相关于卡尔祖-克莱因（KK）理论，该理论假设有额外的空间维度以统一电磁力和引力。在KK理论中，这些额外维度通常被隐藏，并需要高能条件才能探测。受揭示这些维度更可行的挑战启发，本研究将一种扰动势形式\hat{H}_{\ ext{SL}} = βzV_{o_{z}}(θ)应用于具有长度L和半径R_{o}的QPCS。这种势受氢原子中的施特金效应启发，其中能级分裂作为外部影响的指示器。研究显示，在退化配置（R_{o} = \frac{L}{π}）中，施特金-like扰动有效诱导能级分裂，这可以被解释为揭示隐藏维度的手段。在此情形下的第一阶能级修正明确依赖于量子数n_{z}和n_θ，突显了这种方法在低能量子系统中探测额外维度效应的潜力。

英文摘要：

This study explores the influence of a Stark-like perturbative potential on a quantum particle confined to a cylindrical surface (QPCS) and its implications for extra-dimensional theories. The QPCS framework is particularly relevant to Kaluza-Klein (KK) theory, which postulates extra spatial dimensions to unify electromagnetism and gravity. In KK theory, these extra dimensions are typically hidden and require high-energy conditions for detection. Motivated by the challenge of uncovering these dimensions more feasibly, this research applies a perturbative potential of the form \hat{H}_{\text{SL}} = βzV_{o_{z}}(θ) to a QPCS characterized by length \textit{L} and radius R_{o}. This potential is inspired by the Stark effect in hydrogen atoms, where energy level splitting serves as an indicator of an external influence. The study demonstrates that, for a degenerate configuration (R_{o} = \frac{L}π), the Stark-like perturbation effectively induces energy level splitting, which can be interpreted as a means of revealing hidden dimensions. The first-order energy correction in this scenario depends explicitly on the quantum numbers n_{z} and n_θ, highlighting the potential for this approach to probe extra-dimensional effects in lower-energy quantum systems.

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