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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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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Appendix 18 Convergence of Matrix Power Series . Appendix 1C Remarks on Theory of Functions of Complex Variables . 1C.1 1C.2 1C3 1C.4 1C.5 Analytic Functions . . . . . The Cauchy Integral Theorem and Corollary Singularities .
Appendix 18 Convergence of Matrix Power Series . Appendix 1C Remarks on Theory of Functions of Complex Variables . 1C.1 1C.2 1C3 1C.4 1C.5 Analytic Functions . . . . . The Cauchy Integral Theorem and Corollary Singularities .
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There are a finite number of dependent variables (the coordinates of the physical system) and one independent variable (the time). Part One is concerned solely with the solution of such systems of equations for prescribed initial ...
There are a finite number of dependent variables (the coordinates of the physical system) and one independent variable (the time). Part One is concerned solely with the solution of such systems of equations for prescribed initial ...
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... second time derivatives may be eliminated from Eqs. (1.4) by the introduction of the two new dependent variables x3 and x4. mic1 = x3 mic2 = x4 *3 = ko(x2 _ x1) _ kxl 5'4 = ko(X1 — x2) '* kxz um A more fundamental change in the form ...
... second time derivatives may be eliminated from Eqs. (1.4) by the introduction of the two new dependent variables x3 and x4. mic1 = x3 mic2 = x4 *3 = ko(x2 _ x1) _ kxl 5'4 = ko(X1 — x2) '* kxz um A more fundamental change in the form ...
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... by (1.7) and (1.8), the forces F, F1, and F 2 are independent of time, a simpler problem than that of solving the equations of motion suggests itself : What solutions exist in which the dependent variables do not change with time ?
... by (1.7) and (1.8), the forces F, F1, and F 2 are independent of time, a simpler problem than that of solving the equations of motion suggests itself : What solutions exist in which the dependent variables do not change with time ?
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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 |
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