Relativistic Quantum Mechanics
Relativistic Quantum Mechanics begins with the Klein-Gordon equation describing its features and motivating the need for a correct relativistic equation for the electron. It then introduces the Dirac equation by linearizing the second order relativistic equation which reveals the spin, spin magnetic moment and the spin-orbit coupling of the electron. After demonstrating the relativistic covariance of the Dirac equation, the discrete transformations of the Dirac spinor, are explained. The Dirac equation for a free electron and an electron in hydrogen atom are solved these solutions are used to interpret the negative energy states in the hole theory of Dirac. As applications of the Dirac equation, the scattering of electrons by a Coulomb potential is given in detail and extended to electron-proton scattering. As a further application, the Dirac equation with zero mass is considered to describe the neutrino. The chapter on neutrinos contains a brief description of neutrino oscillations . The book ends with giving an elementary treatment of spin manifolds with illustrative examples.
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Solutions to the Dirac Equation
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2-component 4-vector angular momentum anti-commutator becomes beta decay Chapter Chapter.4 charge conjugated chiral commutes components Consider the Dirac constant of motion corresponding cos0 cos2 Coulomb potential coupling covariant derivative denoted described differential cross section Dirac equation Dirac operator Dirac's theory eigenstates eigenvalues evaluated expression F-W transformation final electron follows free particle gamma matrices gauge field given gives hadrons hamiltonian helicity hermitian hydrogen atom infinitesimal integration introduce ip(x Klein-Gordon equation Lorentz group Lorentz transformation magnetic mass term multiplying negative energy solutions neutrino oscillations non-relativistic obtain parallel transport Pauli Phys plane positive energy positron properties proton quantum mechanics quantum number quarks relativistic quantum mechanics result right side rotation satisfies Schrodinger second term seen sin(a sin2 space space-time spin connections spin structure spin-orbit spin-up spinor Substituting tion tp(x vector velocity verified wave function Weak Interaction write z-axis zero