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 16
... mx = my leads to the conclusion that x = y: mesme Ix==ly x=y It is not diflicult to show that if m is nonsingular (i.e., the determinant of m does not vanish) there exists a unique matrix, denoted by m-l, such that mm—1 : m—lm = 1.
... mx = my leads to the conclusion that x = y: mesme Ix==ly x=y It is not diflicult to show that if m is nonsingular (i.e., the determinant of m does not vanish) there exists a unique matrix, denoted by m-l, such that mm—1 : m—lm = 1.
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Let D denote the determinant of m [as given in (1.40) or (1.41)]. For 2 X 2 matrices _ 1 "'22 —m12 m 1 = — (1.44) _ D “'mzt mu For 3 X 3 matrices mzzmaa _ mzamaz m13m32 _ mlzmas ml2m23 _ m13m22 _1 _ _ _ _ m — m23m31 m21m33 mnmaa m13m31 ...
Let D denote the determinant of m [as given in (1.40) or (1.41)]. For 2 X 2 matrices _ 1 "'22 —m12 m 1 = — (1.44) _ D “'mzt mu For 3 X 3 matrices mzzmaa _ mzamaz m13m32 _ mlzmas ml2m23 _ m13m22 _1 _ _ _ _ m — m23m31 m21m33 mnmaa m13m31 ...
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Thus, let the eigencolumns of A be denoted s_,-, so that As, = Ls, (2.10) Further, suppose that there are enough such eigencolumns that one may write, for the specified initial conditions 14(0), “(0) = 5.1111 + 3.2% + ' ' ' = Saar ...
Thus, let the eigencolumns of A be denoted s_,-, so that As, = Ls, (2.10) Further, suppose that there are enough such eigencolumns that one may write, for the specified initial conditions 14(0), “(0) = 5.1111 + 3.2% + ' ' ' = Saar ...
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Thus, let these distinct eigenvalues be denoted 1,, with i taking on a value for each distinct eigenvalue, and let the corresponding eigencolumns be denoted sj. It will be assumed that these eigencolumns are linearly dependent and it ...
Thus, let these distinct eigenvalues be denoted 1,, with i taking on a value for each distinct eigenvalue, and let the corresponding eigencolumns be denoted sj. It will be assumed that these eigencolumns are linearly dependent and it ...
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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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