Poincaré上半平面几何中自由量子粒子的行为
Behavior of a Free Quantum Particle in the Poincaré Upper Half-Plane Geometry
摘要：
受Filho等人最近工作的启发，在具有对角度量的一般弯曲空间中引入了一个厄米特动量算子。计算并讨论了与新动量有关的修正哈密顿量。此外，在给出Heisenberg方程在弯曲空间中的有效性的基础上，推广并解释了Escherichfest定理在弯曲空间中的新的位置相关微分算子.修正后的哈密顿量导出了修正后的与时间无关的薛定谔方程，并在庞加莱上半平面几何中对自由粒子显式求解。它示出，一个“自由粒子”不表现为它是完全自由的，由于弯曲的背景几何形状。
英文摘要：
Inspired by the recent work of Filho et al., a Hermitian momentum operator is introduced in a general curved space with diagonal metric. The modified Hamiltonian associated with this new momentum is calculated and discussed. Furthermore, granting the validity of the Heisenberg equation in a curved space, the Ehrenfest theorem is generalized and interpreted with the new position-dependent differential operator in a curved space. The modified Hamiltonian leads to a modified time-independent Schrödinger equation, which is solved explicitly for a free particle in the Poincaré upper half-plane geometry. It is shown that a "free particle" does not behave as it is totally free due to curved background geometry.
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