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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In Part One of the book, systems with a finite number of degrees of freedom (described by matrices) are considered and studied. In Part Two the concepts developed for discrete systems in Part One are extended to continuous systems.
In Part One of the book, systems with a finite number of degrees of freedom (described by matrices) are considered and studied. In Part Two the concepts developed for discrete systems in Part One are extended to continuous systems.
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16 1.9 Linear Independence 17 Chapter 2 Solution for Diagonalizable Matrices . . . 21 2.1 Solution by Taylor Series . ... 35 Chapter 3 The Evaluation of a Function of a Matrix for an Arbitrary Matrix 38 3.1 Introduction .
16 1.9 Linear Independence 17 Chapter 2 Solution for Diagonalizable Matrices . . . 21 2.1 Solution by Taylor Series . ... 35 Chapter 3 The Evaluation of a Function of a Matrix for an Arbitrary Matrix 38 3.1 Introduction .
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Appendix 18 Convergence of Matrix Power Series . Appendix 1C Remarks on Theory of Functions of Complex Variables . 1C.1 1C.2 1C3 1C.4 1C.5 Analytic Functions . . . . . The Cauchy Integral Theorem and Corollary Singularities .
Appendix 18 Convergence of Matrix Power Series . Appendix 1C Remarks on Theory of Functions of Complex Variables . 1C.1 1C.2 1C3 1C.4 1C.5 Analytic Functions . . . . . The Cauchy Integral Theorem and Corollary Singularities .
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1.3 Matrices In each of the three categories of problems considered in Sec. ... For the purpose of display of the matrix m one writes mu "112 "'13 ' ' ' m1" "121 11122 mm ' ' ' mu m = _ _ _ (1.17) mai "'32 mas m3n mnl mn2 mn3 ' .
1.3 Matrices In each of the three categories of problems considered in Sec. ... For the purpose of display of the matrix m one writes mu "112 "'13 ' ' ' m1" "121 11122 mm ' ' ' mu m = _ _ _ (1.17) mai "'32 mas m3n mnl mn2 mn3 ' .
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Any matrix m for which m,,~ : m,,, i 72 j, is called a symmetric matrix. If m,, = —m,.~, m,,~ : 0, the matrix is said to be antisymmetric or skewsymmetric. The n numbers x, may be considered to form an n X 1 matrix1 or n column, ...
Any matrix m for which m,,~ : m,,, i 72 j, is called a symmetric matrix. If m,, = —m,.~, m,,~ : 0, the matrix is said to be antisymmetric or skewsymmetric. The n numbers x, may be considered to form an n X 1 matrix1 or n column, ...
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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 |