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 10
In this case, the matrices are equal if each element of one equals the corresponding element of the other. Thus, if m and p are matrices and x and y are columns (or rows), m = p implies m,, = pi, all iandj .
In this case, the matrices are equal if each element of one equals the corresponding element of the other. Thus, if m and p are matrices and x and y are columns (or rows), m = p implies m,, = pi, all iandj .
Página 12
... 0 for 1' 7i j The importance of the Kronecker delta arises from (1.34) and from the corresponding property (135) 2 drift =ft (1.36) 1.5 The Row-Column Rule The definition of the product of two matrices, as given by Eqs. (1.29), ...
... 0 for 1' 7i j The importance of the Kronecker delta arises from (1.34) and from the corresponding property (135) 2 drift =ft (1.36) 1.5 The Row-Column Rule The definition of the product of two matrices, as given by Eqs. (1.29), ...
Página 13
Before reaping this benefit from the notation, it is best to consider some of the dangers and corresponding precautions to be used. In this section a few of the ways in which matrices differ in their arithmetic properties from numbers ...
Before reaping this benefit from the notation, it is best to consider some of the dangers and corresponding precautions to be used. In this section a few of the ways in which matrices differ in their arithmetic properties from numbers ...
Página 15
The determinant of 21 — m is a polynomial of degree n in z, with leading term z”, if m is an n X n square matrix, I the corresponding n X n unit matrix, and z a scalar. An immediate consequence of property 5 is the existence of ...
The determinant of 21 — m is a polynomial of degree n in z, with leading term z”, if m is an n X n square matrix, I the corresponding n X n unit matrix, and z a scalar. An immediate consequence of property 5 is the existence of ...
Página 28
Corresponding to each distinct eigenvalue, there exists a nontrivial eigencolumn of A, found by solution of (2.23) after insertion for 11 of the appropriate root of the characteristic equation. It will now be shown that A has at least ...
Corresponding to each distinct eigenvalue, there exists a nontrivial eigencolumn of A, found by solution of (2.23) after insertion for 11 of the appropriate root of the characteristic equation. It will now be shown that A has at least ...
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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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