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 14
This definition yields also a test to tell when a matrix is singular—1e, one need merely evaluate the determinant. It will be seen in Sec. 1.8 that nonsingular matrices have the properties mentioned earlier in this section for nonzero ...
This definition yields also a test to tell when a matrix is singular—1e, one need merely evaluate the determinant. It will be seen in Sec. 1.8 that nonsingular matrices have the properties mentioned earlier in this section for nonzero ...
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CHAPTER 2 Solution for Diagonalizable Matrices 2.1 Solution by Taylor Series A standard method for the solution of the differential equation 12(1) = Au(t) (2.1) yields the solution in the form of a power series in the independent ...
CHAPTER 2 Solution for Diagonalizable Matrices 2.1 Solution by Taylor Series A standard method for the solution of the differential equation 12(1) = Au(t) (2.1) yields the solution in the form of a power series in the independent ...
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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):: ...
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If it so happens that u(0) in (2.4) is an eigencolumn of A, then (2.8) yields immediately u(t) = e'“u(0) = e”u(0) (2.9) It should be noticed that the solution (2.9) is of very simple form. This simple form arises from the accident that ...
If it so happens that u(0) in (2.4) is an eigencolumn of A, then (2.8) yields immediately u(t) = e'“u(0) = e”u(0) (2.9) It should be noticed that the solution (2.9) is of very simple form. This simple form arises from the accident that ...
Página 34
To obtain the equations satisfied by y and z, the two Eqs. (1.4) are added and subtracted to yield m§+kz=0 mi+(k—2ko)Y=0 ... than to calculate S, S—1, and A. If A is singular,l say because 11 = 0, then neither (2.29) nor (2.30) yields ...
To obtain the equations satisfied by y and z, the two Eqs. (1.4) are added and subtracted to yield m§+kz=0 mi+(k—2ko)Y=0 ... than to calculate S, S—1, and A. If A is singular,l say because 11 = 0, then neither (2.29) nor (2.30) yields ...
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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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