Wedges I
The wedge problem, that is, the propagation of radiation or particles in the presence of a wedge, is examined in different contexts. Generally, the paper follows the historical order from Sommerfeld's early work to recent stochastic results - hindsights and new results being woven in as appropriate. In each context, identifying the relevant mathematical problem has been the key to the solution. Thus each section can be given both a physics and a mathematics title: Section 2: diffraction by reflecting wedge; boundary value problem of differential equations; solutions defined on multiply connected spaces. Section 3: geometrical theory of diffraction; identification of function spaces. Section 4: path integral solutions; path integration on multiply connected spaces; asymptotics on the boundaries of function spaces. Section 5: probing the shape of the wedge and the roughness of its surface; stochastic calculus. Several propagators and Green functions are given explicitly, some old ones and some new ones. They include the knife-edge propagator for Dirichlet and Neumann boundary conditions, the absorbing knife edge propagator, the wedge propagators, the propagator for a free particle on a /sigma phi/-sheeted Riemann surface, the Dirichlet and the Neumann wedge Green function.
- Research Organization:
- Univ. of Texas, Austin, TX
- OSTI ID:
- 7242639
- Journal Information:
- Found. Phys.; (United States), Vol. 16:4
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
CHARGED-PARTICLE TRANSPORT
BOUNDARY-VALUE PROBLEMS
QUANTUM MECHANICS
ELECTROMAGNETIC RADIATION
DIFFRACTION
DIRICHLET PROBLEM
FEYNMAN PATH INTEGRAL
FOURIER TRANSFORMATION
GREEN FUNCTION
NEUMANN SERIES
PROPAGATOR
RIEMANN SPACE
SCHROEDINGER EQUATION
SOMMERFELD INTEGRALS
STOCHASTIC PROCESSES
WAVE PROPAGATION
COHERENT SCATTERING
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
INTEGRAL TRANSFORMATIONS
INTEGRALS
MATHEMATICAL SPACE
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
RADIATION TRANSPORT
RADIATIONS
SCATTERING
SERIES EXPANSION
SPACE
TRANSFORMATIONS
WAVE EQUATIONS
657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics
657000 - Theoretical & Mathematical Physics