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 18
Página viii
... Vector Spaces and Linear Operators . . . . 50 4.1 Introduction . 50 4.2 Base Vectors and Basis 52 4.3 Change of ... Space . . . . . 58 4.7 Efl'ect of Change of Basis on the Representation of an Operator 59 4.8 The Spectral Representation ...
... Vector Spaces and Linear Operators . . . . 50 4.1 Introduction . 50 4.2 Base Vectors and Basis 52 4.3 Change of ... Space . . . . . 58 4.7 Efl'ect of Change of Basis on the Representation of an Operator 59 4.8 The Spectral Representation ...
Página 52
... vector will have meaning independent of the coordinate system. 4.2 Base Vectors and Basis It is assumed that the reader is familiar with the concepts of the ordinary three-dimensional vector spaces. As a Starting point, recall that the ...
... vector will have meaning independent of the coordinate system. 4.2 Base Vectors and Basis It is assumed that the reader is familiar with the concepts of the ordinary three-dimensional vector spaces. As a Starting point, recall that the ...
Página 53
... space. Any vector x may be written as2 n x = Z u,x,~ (4.6) i=1 The set of vectors u, is said to form a basis. The x,- are the components of the vector x in this basis. For convenience, this basis will ... VECTOR SPACES AND LINEAR OPERATORS.
... space. Any vector x may be written as2 n x = Z u,x,~ (4.6) i=1 The set of vectors u, is said to form a basis. The x,- are the components of the vector x in this basis. For convenience, this basis will ... VECTOR SPACES AND LINEAR OPERATORS.
Página 54
Alcanzaste el límite de visualización de este libro.
Alcanzaste el límite de visualización de este libro.
Página 55
Alcanzaste el límite de visualización de este libro.
Alcanzaste el límite de visualización de este libro.
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