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Quantum Mechanics with Basic Field Theory by Bipin R. Desai

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33 The Dirac equation

Below we outline the formulation of the Dirac equation incorporating momentum and energy as linear terms in the Hamiltonian. We find that it leads to the prediction of particles with spin 1/2.

33.1 Basic formalism

We found in our discussion on the subject of relativistic quantum mechanics in Chapter 31 that, as a consequence of the quadratic nature of the energy–momentum relation, negative energy solutions must exist and that the probability density is not positive definite. To solve these problems, Dirac set out to write a quantum-mechanical equation that was linear in energy and momentum based on the following Hamiltonian for a free particle,

with m0 the rest mass, p the momentum of the particle and the unknown α and ...

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