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. |
Dentro del libro
Resultados 1-5 de 88
Página 4
The equations of motion are mx'i + kx1 = ko(x2 _ x1) 1.4 mi: + kxz = ko(x1 _ X2) ( ) While examples of this nature may be given indefinitely, those already presented will suffice to give a picture of the situation.
The equations of motion are mx'i + kx1 = ko(x2 _ x1) 1.4 mi: + kxz = ko(x1 _ X2) ( ) While examples of this nature may be given indefinitely, those already presented will suffice to give a picture of the situation.
Página 6
The second category, that of time-dependent inhomogeneous problems, has equations of the form given by (1.16) below. It will be noted that setting F,(t) = 0 reduces these to (1.11). 1 *1 = mllxl + "112x2 '1' ' ' ' + mlnxn + F10) 5'2 ...
The second category, that of time-dependent inhomogeneous problems, has equations of the form given by (1.16) below. It will be noted that setting F,(t) = 0 reduces these to (1.11). 1 *1 = mllxl + "112x2 '1' ' ' ' + mlnxn + F10) 5'2 ...
Página 7
This set of numbers is given a name as an assemblage. The assemblage is said to form a matrix m. The quantities m,,- are called the elements of the matrix m. For the purpose of display of the matrix m one writes mu "112 "'13 ' ' ' m1" ...
This set of numbers is given a name as an assemblage. The assemblage is said to form a matrix m. The quantities m,,- are called the elements of the matrix m. For the purpose of display of the matrix m one writes mu "112 "'13 ' ' ' m1" ...
Página 8
It is clear that for the purposes of display the representations given in (1.17) and (1.18) might well be useful. On the other hand, this is scarcely sufficient advantage to justify strong interest. In order to make full use of the ...
It is clear that for the purposes of display the representations given in (1.17) and (1.18) might well be useful. On the other hand, this is scarcely sufficient advantage to justify strong interest. In order to make full use of the ...
Página 11
The definition will be given here. The product of two matrices is defined only if the number of columns in the matrix on the left is equal to the number of rows in the matrix on the right. The product is then defined by (1.28) ("Ulla ...
The definition will be given here. The product of two matrices is defined only if the number of columns in the matrix on the left is equal to the number of rows in the matrix on the right. The product is then defined by (1.28) ("Ulla ...
Comentarios de la gente - Escribir un comentario
No encontramos ningún comentario en los lugares habituales.
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
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 |
| Exportar cita | BiBTeX EndNote RefMan |