Some Mathematical Methods of PhysicsCourier Corporation, 2014 M03 5 - 320 páginas This 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. |
Dentro del libro
Resultados 1-5 de 20
Página vii
... Eigencolumns . . . . . . . 22 2.3 Superposition . . . . . . . . . . 23 2.4 Completeness . . . . . . . . . . 24 2.5 Diagonalization of Nondegenerate Matrices . . . . 27 2.6 Outline of Computation Procedure with Examples . . . 29 2.7 ...
... Eigencolumns . . . . . . . 22 2.3 Superposition . . . . . . . . . . 23 2.4 Completeness . . . . . . . . . . 24 2.5 Diagonalization of Nondegenerate Matrices . . . . 27 2.6 Outline of Computation Procedure with Examples . . . 29 2.7 ...
Página 22
... Eigencolumns If there exist a number 1 and a column u such that Au = a“ (2.7) then A is said to be an eigenvalue of A , u is said to be an eigencolumn of A , and the eigencolumn u and the eigenvalue 1 are said to belong to each other ...
... Eigencolumns If there exist a number 1 and a column u such that Au = a“ (2.7) then A is said to be an eigenvalue of A , u is said to be an eigencolumn of A , and the eigencolumn u and the eigenvalue 1 are said to belong to each other ...
Página 23
... eigencolumns such that u(()) may be written as a linear combination (superposition) of these eigencolumns. In such a case, a solution almost as simple in form as that of (2.9) is obtained. Thus, let the eigencolumns of A be denoted s_ ...
... eigencolumns such that u(()) may be written as a linear combination (superposition) of these eigencolumns. In such a case, a solution almost as simple in form as that of (2.9) is obtained. Thus, let the eigencolumns of A be denoted s_ ...
Página 24
... eigencolumn and eigenvalue are found to be 1 s.2=(_1) 42=(1_g) The initial conditions, as given by u(0), may now be written in the form indicated in (2.11) as a linear superposition of eigencolumns of A: _.~+d1 c—d 1) to» 2 (.)+ 2 L. It ...
... eigencolumn and eigenvalue are found to be 1 s.2=(_1) 42=(1_g) The initial conditions, as given by u(0), may now be written in the form indicated in (2.11) as a linear superposition of eigencolumns of A: _.~+d1 c—d 1) to» 2 (.)+ 2 L. It ...
Página 25
... eigencolumns of A if and only if A has n linearly independent eigencolumns. Thus, if A has less than n linearly independent eigencolumns, the resultant linear superposition will depend on less than n arbitrary constants, whereas an ...
... eigencolumns of A if and only if A has n linearly independent eigencolumns. Thus, if A has less than n linearly independent eigencolumns, the resultant linear superposition will depend on less than n arbitrary constants, whereas an ...
Otras ediciones - Ver todas
Términos y frases comunes
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