Some Mathematical Methods of PhysicsThis well-rounded, thorough treatment for advanced undergraduates and graduate students introduces basic concepts of mathematical physics involved in the study of linear systems. The text emphasizes eigenvalues, eigenfunctions, and Green's functions. Prerequisites include differential equations and a first course in theoretical physics. The three-part presentation begins with an exploration of systems with a finite number of degrees of freedom (described by matrices). In part two, the concepts developed for discrete systems in previous chapters are extended to continuous systems. New concepts useful in the treatment of continuous systems are also introduced. The final part examines approximation methods — including perturbation theory, variational methods, and numerical methods — relevant to addressing most of the problems of nature that confront applied physicists. Two Appendixes include background and supplementary material. 1960 edition. |
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Página vii
23 2.4 Completeness . . . . . . . . . . 24 2.5 Diagonalization of Nondegenerate Matrices . . . . 27 2.6 Outline of Computation Procedure with Examples . . . 29 2.7 Change of Variable . . . . . . . . . 32 2.8 The Steady-state Solution .
23 2.4 Completeness . . . . . . . . . . 24 2.5 Diagonalization of Nondegenerate Matrices . . . . 27 2.6 Outline of Computation Procedure with Examples . . . 29 2.7 Change of Variable . . . . . . . . . 32 2.8 The Steady-state Solution .
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15.5 Higher Eigenvalues by the Ritz Method 15.6 Example of the Ritz Method Chapter 16 Iteration Procedures 16.1 Introduction . 16.2 Eigenvalue Problems . 16.3 Inverses by Iteration . Chapter 17 Construction of Eigenvalue Problems 17.1 ...
15.5 Higher Eigenvalues by the Ritz Method 15.6 Example of the Ritz Method Chapter 16 Iteration Procedures 16.1 Introduction . 16.2 Eigenvalue Problems . 16.3 Inverses by Iteration . Chapter 17 Construction of Eigenvalue Problems 17.1 ...
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A similar procedure will be used to solve (1.20). It may be argued that (1.21) is, in conjunction with (1.19), no more than a definition of e'"'. If this viewpoint be adopted, the methods of interpretation and evaluation of em' to be ...
A similar procedure will be used to solve (1.20). It may be argued that (1.21) is, in conjunction with (1.19), no more than a definition of e'"'. If this viewpoint be adopted, the methods of interpretation and evaluation of em' to be ...
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... note that none of the above prohibits A from having a complete set of eigencolumns, even if A is degenerate. 2.6 Outline of Computation Procedure with Examples The motivation of 28 SYSTEMS WITH A FINITE NUMBER OF DEGREES OF FREEDOM.
... note that none of the above prohibits A from having a complete set of eigencolumns, even if A is degenerate. 2.6 Outline of Computation Procedure with Examples The motivation of 28 SYSTEMS WITH A FINITE NUMBER OF DEGREES OF FREEDOM.
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2.6 Outline of Computation Procedure with Examples The motivation of the considerations in the last sections was the evaluation of the solution of the equations of motion of a system, as written in the form 12 = Au This solution was ...
2.6 Outline of Computation Procedure with Examples The motivation of the considerations in the last sections was the evaluation of the solution of the equations of motion of a system, as written in the form 12 = Au This solution was ...
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applied approximate arbitrary base vectors basis Bessel function boundary conditions Chap chapter coefficients column commute complete consider constant continuous systems contour corresponding cylindrical functions defined definition denoted determinant diagonal diagonalizable differential equation Dirac notation domain eigen eigencolumns eigenfunctions eigenvalue equation eigenvector elements evaluate expansion find finite number first follows formula Fourier given Green’s function Hence Hermitian matrix Hermitian operator infinite integral Introduction inverse Laplacian linear operator linearly independent lowest eigenvalue matrix McGraw-Hill Book Company membrane method multiplication nonsingular normal normal matrix Note number of degrees obtained orthonormality conditions perturbation plane procedure QUANTUM MECHANICS relations representation result Ritz method satisfies satisfy scattering solve specified spherical spherical harmonics string Substitution theorem theory tion trial functions vanish variable vector space verified wave write written yields York zero
Información bibliográfica
| Título | Some Mathematical Methods of Physics Dover Books on Physics |
| Autores | Gerald Goertzel, Nunzio Tralli |
| Editor | Courier Corporation, 2014 |
| ISBN | 048679332X, 9780486793320 |
| Largo | 320 páginas |
| Exportar cita | BiBTeX EndNote RefMan |