(a) Write down the Dirac equation in Hamiltonian form for a free par- ticle, and give explicit forms for the Dirac matrices. (b) Show that the Hamiltonian H commutes with the operator o · P where P is the momentum operator and o is the Pauli spin operator in the space of four component spinors. (c) Find plane wave solutions of the Dirac equation in the representation in which o . P is diagonal. Here P is the eigenvalue of the momentum operator.
(a) Write down the Dirac equation in Hamiltonian form for a free par- ticle, and give explicit forms for the Dirac matrices. (b) Show that the Hamiltonian H commutes with the operator o · P where P is the momentum operator and o is the Pauli spin operator in the space of four component spinors. (c) Find plane wave solutions of the Dirac equation in the representation in which o . P is diagonal. Here P is the eigenvalue of the momentum operator.
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Transcribed Image Text:(a) Write down the Dirac equation in Hamiltonian form for a fro par-
ticle, and give explicit forms for the Dirac matrices.
(b) Show that the Hamiltonian H commutes with the operator o · P
where P is the momentum operator and o is the Pauli spin operator in the
space of four component spinors.
(c) Find plane wave solutions of the Dirac equation in the representation
in which o . P is diagonal. Here P is the eigenvalue of the momentum
operator.
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