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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13 1.7 Some Properties of Determinants 14 1.8 Inverses . . . . 16 1.9 Linear Independence 17 Chapter 2 Solution for Diagonalizable Matrices . . . 21 2.1 Solution by Taylor Series . . . . . . . . 21 2.2 Eigenvalues and Eigencolumns .
13 1.7 Some Properties of Determinants 14 1.8 Inverses . . . . 16 1.9 Linear Independence 17 Chapter 2 Solution for Diagonalizable Matrices . . . 21 2.1 Solution by Taylor Series . . . . . . . . 21 2.2 Eigenvalues and Eigencolumns .
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16.3 Inverses by Iteration . Chapter 17 Construction of Eigenvalue Problems 17.1 Introduction 17.2 The Method . . . . . 17.3 Application to the Scattering Problem Chapter 18 Numerical Procedures . 18.1 Introduction .
16.3 Inverses by Iteration . Chapter 17 Construction of Eigenvalue Problems 17.1 Introduction 17.2 The Method . . . . . 17.3 Application to the Scattering Problem Chapter 18 Numerical Procedures . 18.1 Introduction .
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... (real or complex) numbers, the following is true of all numbers except zero: the product of two nonzero numbers is not zero; the same factor may be canceled from both sides of an equation; every number (except zero) has an inverse.
... (real or complex) numbers, the following is true of all numbers except zero: the product of two nonzero numbers is not zero; the same factor may be canceled from both sides of an equation; every number (except zero) has an inverse.
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Also, every nonsingular matrix has an inverse. Some of the properties of determinants which will be needed in Sec. 1.8 are summarized in Sec. 1.7. 1.7 Some Properties of Determinants The determinant of a square matrix m is a number ...
Also, every nonsingular matrix has an inverse. Some of the properties of determinants which will be needed in Sec. 1.8 are summarized in Sec. 1.7. 1.7 Some Properties of Determinants The determinant of a square matrix m is a number ...
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Thus, if m is a nonsingular matrix, since ml = m one has from property 4 WI |1 I = lml whence VI = 1 1.8 Inverses We now show that the product of two. 1 The requirement that the solution be unique is a necessary part of the statement of ...
Thus, if m is a nonsingular matrix, since ml = m one has from property 4 WI |1 I = lml whence VI = 1 1.8 Inverses We now show that the product of two. 1 The requirement that the solution be unique is a necessary part of the statement 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 |