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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Resultados 1-5 de 42
Página viii
57 4.5 The Representation of Linear Operators by Matrices 57 4.6 The Operator in the Dual Space . . . . . 58 4.7 Efl'ect of Change of Basis on the Representation of an Operator 59 4.8 The Spectral Representation of an Operator .
57 4.5 The Representation of Linear Operators by Matrices 57 4.6 The Operator in the Dual Space . . . . . 58 4.7 Efl'ect of Change of Basis on the Representation of an Operator 59 4.8 The Spectral Representation of an Operator .
Página xi
The Integral Representations of the General Cylindrical Functions The Integral Representation of the Bessel Function J, The Hankel Functions . . . . Series Expansions at the Origin . The Asymptotic Expansions .
The Integral Representations of the General Cylindrical Functions The Integral Representation of the Bessel Function J, The Hankel Functions . . . . Series Expansions at the Origin . The Asymptotic Expansions .
Página 8
It is clear that for the purposes of display the representations given in (1.17) and (1.18) might well be useful. On the other hand, this is scarcely sufficient advantage to justify strong interest. In order to make full use of the ...
It is clear that for the purposes of display the representations given in (1.17) and (1.18) might well be useful. On the other hand, this is scarcely sufficient advantage to justify strong interest. In order to make full use of the ...
Página 26
2 This is often called the spectral representation of A; the set of eigenvalues is called the spectrum of A. for the n columns of r. 1 HA is singular, 26 SYSTEMS WITH A FINITE NUMBER OF DEGREES OF FREEDOM.
2 This is often called the spectral representation of A; the set of eigenvalues is called the spectrum of A. for the n columns of r. 1 HA is singular, 26 SYSTEMS WITH A FINITE NUMBER OF DEGREES OF FREEDOM.
Página 34
1.1, one is sometimes concerned with the solution of Au = f (2.28) If A is nonsingular, this solution is immediately given by u = A'lf (2-29) It is sometimes convenient to use the spectral representation of A to obtain A-1 or u.
1.1, one is sometimes concerned with the solution of Au = f (2.28) If A is nonsingular, this solution is immediately given by u = A'lf (2-29) It is sometimes convenient to use the spectral representation of A to obtain A-1 or u.
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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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