Quasiclassical Methods by Jeffrey Rauch
This IMA Volume in Mathematics and its Applications QUASICLASICAL METHODS is based on the proceedings of a very successful one-week workshop with the same title, which was an integral part of the 1994-1995 IMA program on Waves and Scattering. We would like to thank Jeffrey Rauch and Barry Simon for their excellent work as organizers of the meeting. We also take this opportunity to thank the National Science Foun- dation (NSF), the Army Research Office (ARO) and the Office of Naval Research (ONR), whose financial support made the workshop possible. A vner Friedman Robert Gulliver v PREFACE There are a large number of problems where qualitative features of a partial differential equation in an appropriate regime are determined by the behavior of an associated ordinary differential equation. The example which gives the area its name is the limit of quantum mechanical Hamil- tonians (Schrodinger operators) as Planck's constant h goes to zero, which is determined by the corresponding classical mechanical system. A sec- ond example is linear wave equations with highly oscillatory initial data. The solutions are described by geometric optics whose centerpiece are rays which are solutions of ordinary differential equations analogous to the clas- sical mechanics equations in the example above. Much recent work has concerned with understanding terms beyond the leading term determined by the quasi classical limit. Two examples of this involve Weyl asymptotics and the large-Z limit of atomic Hamiltonians, both areas of current research.-
Probability and Partial Differential Equations in Modern Applied Mathematics
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Modeling, Stochastic Control, Optimization, and Applications
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Rational Drug Design
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Computational Fluid Dynamics and Reacting Gas Flows
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Mathematics of DNA Structure, Function and Interactions
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Multiparticle Quantum Scattering with Applications to Nuclear, Atomic and Molecular Physics
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Inverse Problems in Wave Propagation
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Free Boundaries in Viscous Flows
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Mathematics in Industrial Problems
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Natural Locomotion in Fluids and on Surfaces
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Twist Mappings and Their Applications
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Codes, Systems, and Graphical Models
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Coding Theory and Design Theory
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Nonlinear Phenomena in Atmospheric and Oceanic Sciences
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Singularities and Oscillations
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Dynamical Issues in Combustion Theory
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Statistical Models in Epidemiology, the Environment, and Clinical Trials
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Pattern Formation in Continuous and Coupled Systems
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Random Sets
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Discrete Probability and Algorithms
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Large-Scale Optimization with Applications
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Nonlinear Optical Materials
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Frontiers in PDE-Constrained Optimization
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Energy Markets and Responsive Grids
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Radar and Sonar
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Theory and Applications of Liquid Crystals
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Classical and Modern Branching Processes
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Symmetric Functionals on Random Matrices and Random Matchings Problems
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Applications of Combinatorics and Graph Theory to the Biological and Social Sciences
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Numerical Algorithms for Modern Parallel Computer Architectures
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Discrete Event Systems, Manufacturing Systems, and Communication Networks
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Hydrodynamic Behavior and Interacting Particle Systems
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Nonlinear Stochastic PDEs
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Shock Induced Transitions and Phase Structures in General Media
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Particulate Flows
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Stochastic Differential Systems, Stochastic Control Theory and Applications
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q-Series and Partitions
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Signal Processing
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Mathematical Approaches to Biomolecular Structure and Dynamics
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Recent Advances in Iterative Methods
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Mathematical Frontiers in Computational Chemical Physics
Simon, Barry: - Barry Simon is IBM Professor of Mathematics and Theoretical Physics at the California Institute of Technology.
| SKU | Unavailable |
| ISBN 13 | 9781461273493 |
| ISBN 10 | 1461273498 |
| Title | Quasiclassical Methods |
| Author | Jeffrey Rauch |
| Series | The Ima Volumes In Mathematics And Its Applications |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Springer-Verlag New York Inc. |
| Year published | 2012-10-02 |
| Number of pages | 230 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |