Analysis of One and Two Particle Quantum Systems using Geometric Algebra

Abstract

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 two 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 in the geometric algebra setting, which has the advantage of suggesting a generalisation to n subsystems.