Exact Solutions of Relativistic Wave Equations [Paperback]

1. General properties of solutions of the Klein-Gordon and Dirac equations.- 1 Basic notations and equations.- 2 Some properties of the Dirac matrices, scalar product of relativistic wave functions and transformation laws.- 3 On relations between solutions of the Dirac and Klein-Gordon equations.- 4 Spin operators for the Dirac equation.- 2. Most important exactly solvable problems in relativistic quantum mechanics.- 5 Free relativistic particle. ?1.- 6 Motion of charge in a constant and homogeneous magnetic field. ?2.- 7 Motion of charge in the plane-wave electromagnetic field. ?3.- 8 Solutions in spherically symmetric fields. ?4.- 3. Exact solutions of relativistic equations of motion in external fields of special configuration.- 9 General properties of motion of an electron in a crossed electromagnetic field.- 10 Electron in crossed stationary electromagnetic fields. ??5  7.- 11 Exact solutions for a charge in nonstationary crossed fields. ??8  19.- 12 Charge motion in longitudinal electromagnetic fields. ??20  25.- 13 Electron motion in a combination of crossed and longitudinal fields. ??2639.- 14 Exact solutions in the fields of nonstandard structure. ??40  43.- 4. Greens functions of relativistic wave equations in external electromagnetic fields.- 15 Introduction.- 16 Proper-time solution of equations for the Greens functions in a constant field and in a combination of the latter with a plane-wave field.- 17 Solutions and evolution functions of the Klein-Gordon and Dirac equations in a constant field and in its combination with a plane-wave field.- 5. Coherent states of relativistic particles.- 18 Introduction.- 19 Coherent states of relativistic particles that move in an external electromagnetic field.- 6. Charged particles in a quantized plane-wave field.- 20 Basic equations and their interpretation.- 21 Separation of the spin variables in the Dirac equation.- 22 Separation of the spatial and photon variables. Conserved energy-momentum operator of thel4