论文标题
庞加莱上半平面几何形状中游离量子粒子的行为
Behavior of a Free Quantum Particle in the Poincaré Upper Half-Plane Geometry
论文作者
论文摘要
受到Filho等人最近的工作的启发，在具有对角线度量的一般弯曲空间中引入了Hermitian动量操作员。与这种新势头相关的修改后的汉密尔顿人进行了计算和讨论。此外，在弯曲的空间中授予海森堡方程的有效性，Ehrenfest定理被广泛化并用弯曲空间中的新位置依赖差分运算符进行了解释。修改后的汉密尔顿人导致了修改时间与时间独立的Schrödinger方程，该方程是针对庞加莱上半平面几何形状中的自由粒子明确求解的。结果表明，由于弯曲的背景几何形状，“自由粒子”的行为不完全自由。
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.
