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 8
That is, the solution to Eq. (1.19) may be written as x(t) = e'"'x(0) (1.21) The interpretation of this result is, in fact, the main subject matter of this book. A similar procedure will be used to solve (1.20).
That is, the solution to Eq. (1.19) may be written as x(t) = e'"'x(0) (1.21) The interpretation of this result is, in fact, the main subject matter of this book. A similar procedure will be used to solve (1.20).
Página 10
Thus, suppose it is desired to evaluate 22,2, where Zr 2 mia'xi J The result is obtained by the following processes: 2 252 2 Z zizi = 'niixj) mikxk) i i k 2 2 mijmikxixk i,.'i,k It is to be noted that 2, was written once with j as the ...
Thus, suppose it is desired to evaluate 22,2, where Zr 2 mia'xi J The result is obtained by the following processes: 2 252 2 Z zizi = 'niixj) mikxk) i i k 2 2 mijmikxixk i,.'i,k It is to be noted that 2, was written once with j as the ...
Página 12
To understand this rule, one might consider the result it gives for the product of a l X n matrix (row) 2 with an n X 1- matrix (column) x. The result is a 1 X 1 matrix zx given by 2x = Zzixi (1.37) i=1 In words the prescription ...
To understand this rule, one might consider the result it gives for the product of a l X n matrix (row) 2 with an n X 1- matrix (column) x. The result is a 1 X 1 matrix zx given by 2x = Zzixi (1.37) i=1 In words the prescription ...
Página 22
As a brief calculation based on (2.7) will convince the reader, this definition yields the following result for f(A)u: f(A)u = i i d—nf- (A — aI)"u “=0 n! dx” F, _ 1 d"f - . _ Fag. —~ a) it From (2.5) it follows that f(A)“ =f (1):: ...
As a brief calculation based on (2.7) will convince the reader, this definition yields the following result for f(A)u: f(A)u = i i d—nf- (A — aI)"u “=0 n! dx” F, _ 1 d"f - . _ Fag. —~ a) it From (2.5) it follows that f(A)“ =f (1):: ...
Página 23
The result (2.8) which defines f(A) as it acts on any eigencolumn of A may be applied to such f for which convergent power series do not exist, provided that the right side of (2.8) is meaningful. 2.3 Superposition The problem under ...
The result (2.8) which defines f(A) as it acts on any eigencolumn of A may be applied to such f for which convergent power series do not exist, provided that the right side of (2.8) is meaningful. 2.3 Superposition The problem under ...
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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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