Some Mathematical Methods of PhysicsThis 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
50 4.2 Base Vectors and 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 ...
50 4.2 Base Vectors and 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 ...
Página xiii
In addition, we would like to call the attention of the reader to several general references which cover the field of mathematical methods of physics more completely than this book and serve to form the basis of a useful reference ...
In addition, we would like to call the attention of the reader to several general references which cover the field of mathematical methods of physics more completely than this book and serve to form the basis of a useful reference ...
Página 22
a) it From (2.5) it follows that f(A)“ =f (1):: (2.8) The result given in (2.8), which holds for any u which is an eigencolumn of A [i.e. , any u satisfying (2.7)], and for any f with convergent-power-series expansion, will be the basis ...
a) it From (2.5) it follows that f(A)“ =f (1):: (2.8) The result given in (2.8), which holds for any u which is an eigencolumn of A [i.e. , any u satisfying (2.7)], and for any f with convergent-power-series expansion, will be the basis ...
Página 52
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 position of a particle in a given cartesian 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 position of a particle in a given cartesian coordinate system ...
Página 53
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 be called the “u, basis” rather than by ...
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 be called the “u, basis” rather than by ...
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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
Información bibliográfica
| Título | Some Mathematical Methods of Physics Dover Books on Physics |
| Autores | Gerald Goertzel, Nunzio Tralli |
| Editor | Courier Corporation, 2014 |
| ISBN | 048679332X, 9780486793320 |
| Largo | 320 páginas |
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