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 ix
11.10 Heat Conduction in an Infinite Solid Chapter 12 12.1 12.2 12.3 12.4 12.5 Green's Functions Definition . . . . . . . . . The Necessary and Sufficient Condition for a Green's Function The Operator —-m2d2/dx2 + I in an Infinite ...
11.10 Heat Conduction in an Infinite Solid Chapter 12 12.1 12.2 12.3 12.4 12.5 Green's Functions Definition . . . . . . . . . The Necessary and Sufficient Condition for a Green's Function The Operator —-m2d2/dx2 + I in an Infinite ...
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One may also define rectangular matrices. Thus, if 11,-,- is defined for all pairs of valuesiandjsuchthati = 1,2,3,. . . ,p,andj = 1,2,. . . ,n,thentheset of pn numbers q,, is said to form a rectangular p X n matrix.
One may also define rectangular matrices. Thus, if 11,-,- is defined for all pairs of valuesiandjsuchthati = 1,2,3,. . . ,p,andj = 1,2,. . . ,n,thentheset of pn numbers q,, is said to form a rectangular p X n matrix.
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In order to make full use of the potentialities of the new symbols, it is necessary to define rules for their manipulation. Such rules will be presented in some detail in Sec. 1.4. These rules are so set up that, in terms of the matrix ...
In order to make full use of the potentialities of the new symbols, it is necessary to define rules for their manipulation. Such rules will be presented in some detail in Sec. 1.4. These rules are so set up that, in terms of the matrix ...
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The summation symbol 2 is defined by the equation anfi :1. +1. + ~ ~ ~ +1.. (123) The power of this notation may be indicated by utilizing it for writing the set of Eqs. (1.16) in the abbreviated form xi: 2 mijxj—I—Fifl) i=l,2,...,n ...
The summation symbol 2 is defined by the equation anfi :1. +1. + ~ ~ ~ +1.. (123) The power of this notation may be indicated by utilizing it for writing the set of Eqs. (1.16) in the abbreviated form xi: 2 mijxj—I—Fifl) i=l,2,...,n ...
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'7' The results of various arithmetic operations with matrices will now be defined. First, the equality of two matrices will be discussed. Two matrices may be equated only if each has the same number of columns and the same number of ...
'7' The results of various arithmetic operations with matrices will now be defined. First, the equality of two matrices will be discussed. Two matrices may be equated only if each has the same number of columns and the same number of ...
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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 |
| Exportar cita | BiBTeX EndNote RefMan |