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 6-10 de 20
Página 26
... eigencolumns of A, belonging to the eigenvalues 1,, be written as s_,. Then, as follows from (2.8), f(A)s.i = S.tf(71.~) (217) To find f(A) from (2.17) is a straightforward matter: f(A) = f(A)] = f(A) 2 S..~(s_l)i. = Z 5.5/(19(8'11 ...
... eigencolumns of A, belonging to the eigenvalues 1,, be written as s_,. Then, as follows from (2.8), f(A)s.i = S.tf(71.~) (217) To find f(A) from (2.17) is a straightforward matter: f(A) = f(A)] = f(A) 2 S..~(s_l)i. = Z 5.5/(19(8'11 ...
Página 27
... eigencolumns as it has distinct eigenvalues, so that if A is nondegenerate it is certain that A may be diagonalized. The best way to find the eigenvalues of A is by trying to find one of the eigencolumns of A. By definition, an eigencolumn ...
... eigencolumns as it has distinct eigenvalues, so that if A is nondegenerate it is certain that A may be diagonalized. The best way to find the eigenvalues of A is by trying to find one of the eigencolumns of A. By definition, an eigencolumn ...
Página 28
... eigencolumns are linearly dependent and it will be shown that this assumption leads to a contradiction. If the eigencolumns are linearly dependent, there exists a set of numbers a,, not all zero, such that 2 3,11,. = 0 (2.25) The ...
... eigencolumns are linearly dependent and it will be shown that this assumption leads to a contradiction. If the eigencolumns are linearly dependent, there exists a set of numbers a,, not all zero, such that 2 3,11,. = 0 (2.25) The ...
Página 29
... eigencolumns of A. That is, solve the n sets of equations (A—1,)s,,-=O i=1,2,...,n one set for each eigencolumn s_,~, belonging to the eigenvalue 2,. Step 3 Express the given u(O) as a linear combination of the eigencolumns of A. That ...
... eigencolumns of A. That is, solve the n sets of equations (A—1,)s,,-=O i=1,2,...,n one set for each eigencolumn s_,~, belonging to the eigenvalue 2,. Step 3 Express the given u(O) as a linear combination of the eigencolumns of A. That ...
Página 30
... eigencolumns remains an eigencolumn when multiplied by any nonzero scalar. This implies, given any s, that the matrix sd is equally valid, provided that d is a nonsingular diagonal matrix. In step 3a, in place of sr = 1, one finds the ...
... eigencolumns remains an eigencolumn when multiplied by any nonzero scalar. This implies, given any s, that the matrix sd is equally valid, provided that d is a nonsingular diagonal matrix. In step 3a, in place of sr = 1, one finds the ...
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