Quantum spin manifests intrinsic angular momentum from "summary" of The Principles of Quantum Mechanics by P. A. M. Dirac
In quantum mechanics, the concept of spin arises as a natural consequence of the wave equation for an electron. This wave equation, known as the Dirac equation, predicts the existence of particles with intrinsic angular momentum, which we call spin. Quantum spin is a fundamental property of particles, much like mass or charge. It is not related to the particle's actual spinning motion, but rather represents an intrinsic angular momentum that cannot be explained by classical physics.
When we say that quantum spin manifests intrinsic angular momentum, what we mean is that particles with spin exhibit properties similar to those of objects in classical mechanics that possess angular momentum. For example, particles with spin can interact with magnetic fields in a way that is analogous to how objects with angular momentum interact with rotational forces.
The quantization of spin, meaning that it can only take on certain discrete values, is a crucial aspect of quantum mechanics. This quantization is a direct consequence of the wave nature of particles and is not something that can be explained classically.
In summary, quantum spin is a fundamental property of particles that manifests as intrinsic angular momentum. This property is essential for understanding the behavior of particles at the quantum level and plays a significant role in many physical phenomena.
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