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 38
... formula from complex variable theory.1 1 f (Z) f(A) 2111' c z - A dz (3'1) This formula may be applied to matrices2 as well as to numbers, provided the contour C encloses all eigenvalues of A and no singularities of f(Z).
... formula from complex variable theory.1 1 f (Z) f(A) 2111' c z - A dz (3'1) This formula may be applied to matrices2 as well as to numbers, provided the contour C encloses all eigenvalues of A and no singularities of f(Z).
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=f(A) The second case to be considered is that where a contour C exists enclosing each zero of IZ — AI and such that 1(2) =§oa.z" on C. Then L AZ). dz = an _1_ Z dz 211i oZ—A "=0 21ri cZ—A provided the series converges.
=f(A) The second case to be considered is that where a contour C exists enclosing each zero of IZ — AI and such that 1(2) =§oa.z" on C. Then L AZ). dz = an _1_ Z dz 211i oZ—A "=0 21ri cZ—A provided the series converges.
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Appendix 1B), whence, for a contour C' on each point of which the series converges, 1 Z” 1 1 A - d =- z"(- - ~--)dZ=A" 211i 0' Z — A 2111' 0' Z + Z2 + But § =§ C 0' Thus (3.5) is proved. 3.4 Evaluation of f(A) with Illustrations Let the ...
Appendix 1B), whence, for a contour C' on each point of which the series converges, 1 Z” 1 1 A - d =- z"(- - ~--)dZ=A" 211i 0' Z — A 2111' 0' Z + Z2 + But § =§ C 0' Thus (3.5) is proved. 3.4 Evaluation of f(A) with Illustrations Let the ...
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... contour of integration surrounded 1 + e and 1 — 6 but not 0 since l/Z is not analytic at Z = 0. As a second illustration consider Example 2. (~15 12) A: ~24 19 From (z _ 4),] = 1 Example 2 . Z—~19 we obtain t111 — m _ 12 q"_zz-4z+3.
... contour of integration surrounded 1 + e and 1 — 6 but not 0 since l/Z is not analytic at Z = 0. As a second illustration consider Example 2. (~15 12) A: ~24 19 From (z _ 4),] = 1 Example 2 . Z—~19 we obtain t111 — m _ 12 q"_zz-4z+3.
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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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