From the Quantum Mechanical State Space to the Position and Momentum Spaces through a Simple Relation

摘要

In an attempt to address the need for an alternative presentation of the quantum mechanical position and momentum spaces, we provide a presentation that is more constructive and less calculative than those found in literature. Our approach is based on a simple, intuitively-understood relation that expresses the physical equivalence of the quantum mechanical state space to the position and momentum spaces. With this work, we hope to offer a perspective complementary to those found in standard quantum mechanics textbooks.