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
9 1.5 The Row-Column Rule . . . . 12 1.6 Warnings. . . . . 13 1.7 Some Properties of Determinants 14 1.8 Inverses . . . . 16 1.9 Linear Independence 17 Chapter 2 Solution for Diagonalizable Matrices . . . 21 2.1 Solution by Taylor ...
9 1.5 The Row-Column Rule . . . . 12 1.6 Warnings. . . . . 13 1.7 Some Properties of Determinants 14 1.8 Inverses . . . . 16 1.9 Linear Independence 17 Chapter 2 Solution for Diagonalizable Matrices . . . 21 2.1 Solution by Taylor ...
Página 7
"Inn To find the element m,, one looks at the intersection of the ith row with the jth column. The matrix m is a square matrix, having as many rows as columns. One may also define rectangular matrices. Thus, if 11,-,- is defined for all ...
"Inn To find the element m,, one looks at the intersection of the ith row with the jth column. The matrix m is a square matrix, having as many rows as columns. One may also define rectangular matrices. Thus, if 11,-,- is defined for all ...
Página 8
The n numbers x, may be considered to form an n X 1 matrix1 or n column, so that one may write x' X1 X2 X2 x : x3 it = x3 (1.18) xn )2" Similarly, the n quantities F I(t) appearing in (1.16) will be represented by the n-column F (t).
The n numbers x, may be considered to form an n X 1 matrix1 or n column, so that one may write x' X1 X2 X2 x : x3 it = x3 (1.18) xn )2" Similarly, the n quantities F I(t) appearing in (1.16) will be represented by the n-column F (t).
Página 10
Two matrices may be equated only if each has the same number of columns and the same number of rows as the other. In this case, the matrices are equal if each element of one equals the corresponding element of the other.
Two matrices may be equated only if each has the same number of columns and the same number of rows as the other. In this case, the matrices are equal if each element of one equals the corresponding element of the other.
Página 11
The product of two matrices is defined only if the number of columns in the matrix on the left is equal to the number of rows in the matrix on the right. The product is then defined by (1.28) ("Ulla = 2 mtkPkt " (1.29) (mx)r = 2 maxi i ...
The product of two matrices is defined only if the number of columns in the matrix on the left is equal to the number of rows in the matrix on the right. The product is then defined by (1.28) ("Ulla = 2 mtkPkt " (1.29) (mx)r = 2 maxi i ...
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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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