An Introduction To Inverse Problems In PhysicsWorld Scientific, 21 May 2020 - 388 sayfa This book is a compilation of different methods of formulating and solving inverse problems in physics from classical mechanics to the potentials and nucleus-nucleus scattering. Mathematical proofs are omitted since excellent monographs already exist dealing with these aspects of the inverse problems.The emphasis here is on finding numerical solutions to complicated equations. A detailed discussion is presented on the use of continued fractional expansion, its power and its limitation as applied to various physical problems. In particular, the inverse problem for discrete form of the wave equation is given a detailed exposition and applied to atomic and nuclear scattering, in the latter for elastic as well as inelastic collision. This technique is also used for inverse problem of geomagnetic induction and one-dimensional electrical conductivity. Among other topics covered are the inverse problem of torsional vibration, and also a chapter on the determination of the motion of a body with reflecting surface from its reflection coefficient. |
İçindekiler
| 1 | |
| 5 | |
2 Inverse Problems in Semiclassical Formulation of Quantum Mechanics | 39 |
3 Inverse Problems and the Heisenberg Equations of Motion | 47 |
4 Inverse Scattering Problem for the Schrodinger Equation and the GelfandLevitan Formulation | 55 |
5 Marchenkos Formulation of the Inverse Scattering Problem | 83 |
6 NewtonSabatier Approach to the Inverse Problem at Fixed Energy | 115 |
7 Discrete Forms of the Schrodinger Equation and the Inverse Problem | 153 |
12 Inverse Problems in Quantum Tunneling | 217 |
13 Inverse Problems Related to the Classical Wave Propagation | 241 |
14 The Inverse Problem of Torsional Vibration | 285 |
15 Local NucleonNucleon Potentials Found from the Inverse Scattering Problem at Fixed Energy | 293 |
16 The Inverse Problem of NucleonNucleus Scattering | 317 |
17 Two Inverse Problems of Electrical Conductivity in Geophysics | 333 |
18 Determination of the Mass Density Distribution Inside or on the Surface of a Body from the Measurement of the External Potential | 349 |
19 The Inverse Problem of Reflection from a Moving Object | 355 |
8 R Matrix Theory and Inverse Problems | 173 |
9 Solvable Models of FokkerPlanck Equation Obtained Using the GelfandLevitan Method | 187 |
10 The Eikonal Approximation | 195 |
11 Inverse Methods Applied to Study Symmetries and Conservation Laws | 207 |
A Expansion Algorithm for Continued Jfractions | 361 |
B Reciprocal Differences of a Quotient and Thieles Theorem | 367 |
| 371 | |
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analytic assume asymptotic form bound boundary condition calculate Chapter choose classical continued fraction defined denote density determine difference equation differential equation direct problem discussed eigenfunctions eigenvalues equations of motion expression Figure finite fixed energy formulation Gel’fand–Levitan given Hamiltonian impact parameter inhomogeneous medium input integral equation intentionally left blank inverse problem Jost function Jost solution Lagrangian let us consider linear logarithmic derivative Marchenko matrix elements normalization constant obtain one-dimensional oscillator Padé approximant partial wave particle phase shift Phys polynomials potential v(r Quantum Mechanics Quantum Scattering Razavy reflection coefficient relation replace result of inversion satisfies Scattering Theory Schrödinger equation shown ſº solvable solve the inverse Springer-Verlag substituting symmetric transform values wave equation wave function wave number write zero