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. |
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Página viii
... Basis 52 4.3 Change of Basis . . 55 4.4 Linear Operators . . . . . . 57 4.5 The Representation of Linear Operators by Matrices 57 4.6 The Operator in the Dual Space . . . . . 58 4.7 Efl'ect of Change of Basis on the Representation of an ...
... Basis 52 4.3 Change of Basis . . 55 4.4 Linear Operators . . . . . . 57 4.5 The Representation of Linear Operators by Matrices 57 4.6 The Operator in the Dual Space . . . . . 58 4.7 Efl'ect of Change of Basis on the Representation of an ...
Página xiii
... basis of a useful reference library. These are listed below in order of their difficulty. Karman, T. V., and M. A. Biot: “Mathematical Methods in Engineering,” McGraw-Hill Book Company, Inc., New York, 1940. Margenau, H., and G. M. ...
... basis of a useful reference library. These are listed below in order of their difficulty. Karman, T. V., and M. A. Biot: “Mathematical Methods in Engineering,” McGraw-Hill Book Company, Inc., New York, 1940. Margenau, H., and G. M. ...
Página 22
... satisfying (2.7)], and for any f with convergent-power-series expansion, will be the basis of the work in the remainder of this chapter and in much of the remainder of this book. The. 22 SYSTEMS wrrn A FINITE NUMBER OF DEGREES 0F FREEDOM.
... satisfying (2.7)], and for any f with convergent-power-series expansion, will be the basis of the work in the remainder of this chapter and in much of the remainder of this book. The. 22 SYSTEMS wrrn A FINITE NUMBER OF DEGREES 0F FREEDOM.
Página 52
... 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 position of a particle in a given cartesian coordinate system OXYZ is given by the ...
... 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 position of a particle in a given cartesian coordinate system OXYZ is given by the ...
Página 53
... basis. For convenience, this basis will be called the “u, basis” rather than by the more cumbersome expression, “the basis in which the u, are the base vectors.” A length may be defined for the vector x. This length should (1) reduce to ...
... basis. For convenience, this basis will be called the “u, basis” rather than by the more cumbersome expression, “the basis in which the u, are the base vectors.” A length may be defined for the vector x. This length should (1) reduce to ...
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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