1粒子和2粒子量子系统的几何代数分析
Analysis of 1 and 2 Particle Quantum Systems using Geometric Algebra
摘要：
当一个量子系统的两个或多个子系统相互作用时，它们可能会纠缠在一起。在这种情况下，各个子系统不再能被描述为纯量子态。对于只有两个子系统的系统，这种纠缠可以用施密特分解来描述。这选择了一个优选的正交基来表达波函数，并给出了系统中存在的纠缠度的度量。这个扩展到更一般的情况下n个子系统还不知道。我们提出了一个审查这个过程中使用的标准表示，并将这种方法应用到几何代数表示。后一种形式的优点是建议推广到n个子系统。
英文摘要：
When two or more subsystems of a quantum system interact with each other they can become entangled. In this case the individual subsystems can no longer be described as pure quantum states. For systems with only 2 subsystems this entanglement can be described using the Schmidt decomposition. This selects a preferred orthonormal basis for expressing the wavefunction and gives a measure of the degree of entanglement present in the system. The extension of this to the more general case of n subsystems is not yet known. We present a review of this process using the standard representation and apply this method to the geometric algebra representation. This latter form has the advantage of suggesting a generalisation to n subsystems.
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