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Exact Solutions of Relativistic Wave Equations

'Mathematics and Its Applications'. Auflage 1990. Book.…
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Titel: Exact Solutions of Relativistic Wave Equations

ISBN: 079230215X
EAN: 9780792302155
'Mathematics and Its Applications'.
Auflage 1990.
Book.
Sprache: Englisch.
Herausgegeben von V. G. Bagrov, D. Gitman
Springer Netherlands

28. Februar 1990 - gebunden - 334 Seiten

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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. §§26-39.- 14 Exact solutions in the fields of nonstandard structure. §§40 - 43.-
4. Green's functions of relativistic wave equations in external electromagnetic fields.- 15 Introduction.- 16 Proper-time solution of equations for the Green's 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 the system.- 23 Charge in quantized field of a monochromatic plane wave with arbitrary polarization.- 24 Decomposition in linear polarizations for a quantized wave with arbitrary spectral composition and polarization.- 25 Canonical forms of the Hamiltonian for quantized wave of general form.- 26 Coordinate representation. Reduction of the Hamiltonian to the canonical form in the coordinate representation.- 27 Stationary states.- 28 Relations of orthogonality, normalization and completeness.- 29 Integrals of motion. Coherent states.- 30 Relation between the Volkov solutions and the wave functions in a quantized plane-wave field.- 31 The Green's functions of the Klein-Gordon and Dirac equations in a quantized plane-wave field.- 32 Charge in the quantized plane-wave field combined with a classical electromagnetic field.-
7. Exact solutions of Dirac-Pauli equations.- 33 The Dirac-Pauli equation.- 34 A charged particle with the anomalous moments in a constant and homogeneous magnetic field.- 35 Exact solutions of the Dirac-Pauli equation for a particle in a plane electromagnetic wave field.- 36 Solution of the Dirac-Pauli equation in a plane-wave field combined with a longitudinal running electric field.- Appendix I Exact solutions of the one-dimensional stationary Schrödinger equation.- Appendix II Systems with quadratic Hamiltonians.- References.
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