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
35 Chapter 3 The Evaluation of a Function of a Matrix for an Arbitrary Matrix 38 3.1 Introduction . . . . . . . . . . 38 3.2 The Cauchy-integral Formula . . . . . . . 38 3.3 Application to Matrices . . . . . . . . 39 3.4 Evaluation of ...
35 Chapter 3 The Evaluation of a Function of a Matrix for an Arbitrary Matrix 38 3.1 Introduction . . . . . . . . . . 38 3.2 The Cauchy-integral Formula . . . . . . . 38 3.3 Application to Matrices . . . . . . . . 39 3.4 Evaluation of ...
Página 25
It is clear that if f(A) is a known matrix, the value of f(A)u is known-for arbitrary u, since the indicated multiplication ... it is clear that the ability to write an arbitrary column u as a linear combination of the eigenvectors of A ...
It is clear that if f(A) is a known matrix, the value of f(A)u is known-for arbitrary u, since the indicated multiplication ... it is clear that the ability to write an arbitrary column u as a linear combination of the eigenvectors of A ...
Página 27
2.5 Diagonalization of Nondegenerate Matrices In the past few sections it has been indicated that a knowledge of the eigenvalues and eigencolumns of a matrix A enables the evaluation of arbitrary functions of the matrix A, provided only ...
2.5 Diagonalization of Nondegenerate Matrices In the past few sections it has been indicated that a knowledge of the eigenvalues and eigencolumns of a matrix A enables the evaluation of arbitrary functions of the matrix A, provided only ...
Página 35
The solution, in terms of u, may now be written: 14 = $0 = Z S_,~v, = 5.101 + Zs.i4i—I(S_l)t.f i=2 where n1 is an arbitrary constant. 2.9 The Inhomogeneous Problem A problem often of interest is to determine u(t), given u(O), ...
The solution, in terms of u, may now be written: 14 = $0 = Z S_,~v, = 5.101 + Zs.i4i—I(S_l)t.f i=2 where n1 is an arbitrary constant. 2.9 The Inhomogeneous Problem A problem often of interest is to determine u(t), given u(O), ...
Página 38
CHAPTER 3 The Evaluation of a Function of a Matrix for an Arbitrary Matrix 3.1 Introduction In Chap. 2 the evaluation of functions of matrices was based on the following relation: If AS = SA then f (A)S = Sf(A) This method was then ...
CHAPTER 3 The Evaluation of a Function of a Matrix for an Arbitrary Matrix 3.1 Introduction In Chap. 2 the evaluation of functions of matrices was based on the following relation: If AS = SA then f (A)S = Sf(A) This method was then ...
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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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