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 15
Página 7
... diagonal of the matrix m are the diagonal elements of m; the remaining elements are the ofldiagonal elements of m. A matrix all of whose offdiagonal elements are zeros is called a diagonal matrix. Any matrix m for which m,,~ : m,,, i 72 ...
... diagonal of the matrix m are the diagonal elements of m; the remaining elements are the ofldiagonal elements of m. A matrix all of whose offdiagonal elements are zeros is called a diagonal matrix. Any matrix m for which m,,~ : m,,, i 72 ...
Página 11
... distinct matrices I are involved in (1.33). The unit matrix I has the following form—all of (1.32) its elements along the main diagonal (the elements Ikk) are FORMULATION OF THE PROBLEM AND DEVELOPMENT or NOTATION II.
... distinct matrices I are involved in (1.33). The unit matrix I has the following form—all of (1.32) its elements along the main diagonal (the elements Ikk) are FORMULATION OF THE PROBLEM AND DEVELOPMENT or NOTATION II.
Página 12
Gerald Goertzel, Nunzio Tralli. its elements along the main diagonal (the elements Ikk) are unity and all others are zero. That is Ii,- = 6,, (1.34) where the symbol 6,,- is the Kronecker delta symbol and is defined by the following ...
Gerald Goertzel, Nunzio Tralli. its elements along the main diagonal (the elements Ikk) are unity and all others are zero. That is Ii,- = 6,, (1.34) where the symbol 6,,- is the Kronecker delta symbol and is defined by the following ...
Página 20
... diagonal matrices of the same order; i.e., show that diagonal matrices commute with one another. 11. Show that if a matrix A commutes with another matrix B, then A commutes with any matrix of the form F(B) = Z an" where n is a positive ...
... diagonal matrices of the same order; i.e., show that diagonal matrices commute with one another. 11. Show that if a matrix A commutes with another matrix B, then A commutes with any matrix of the form F(B) = Z an" where n is a positive ...
Página 26
... diagonal matrix (with diagonal elements 2,) is introduced as1 [f(A)]u = f (it-)6” (218) Then the definition of s becomes As = sA (2.19) where A is specified to be diagonal. Further f(A)S = SKA) (2.20) replaces (2.17). To evaluate f(A) ...
... diagonal matrix (with diagonal elements 2,) is introduced as1 [f(A)]u = f (it-)6” (218) Then the definition of s becomes As = sA (2.19) where A is specified to be diagonal. Further f(A)S = SKA) (2.20) replaces (2.17). To evaluate f(A) ...
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