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 vii
35 Chapter 3 The Evaluation of a Function of a Matrix for an Arbitrary Matrix 38 3.1 Introduction . . . . . . . . . . 38 3.2 The Cauchy-integral Formula . . . . . . . 38 3.3 Application to Matrices . . . . . . . . 39 3.4 Evaluation of ...
35 Chapter 3 The Evaluation of a Function of a Matrix for an Arbitrary Matrix 38 3.1 Introduction . . . . . . . . . . 38 3.2 The Cauchy-integral Formula . . . . . . . 38 3.3 Application to Matrices . . . . . . . . 39 3.4 Evaluation of ...
Página x
The Theorem of Residues . 184 185 190 192 201 201 202 203 204 205 206 207 211 211 212 213 215 220 221 225 225 229 233 233 233 234 236 236 . 236 . 239 243 252 +u: Appendix 2A Evaluation of Integrals of the Form F(x)e"“.
The Theorem of Residues . 184 185 190 192 201 201 202 203 204 205 206 207 211 211 212 213 215 220 221 225 225 229 233 233 233 234 236 236 . 236 . 239 243 252 +u: Appendix 2A Evaluation of Integrals of the Form F(x)e"“.
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+u: Appendix 2A Evaluation of Integrals of the Form F(x)e"“ dx -KO Appendix 2B Fourier Transforms, Integrals, and Series 2B.1 2B.2 2B.3 2B.4 2B.5 213.6 2B.7 Introduction Transforms . . . . Infinite One-dimensional Transforms .
+u: Appendix 2A Evaluation of Integrals of the Form F(x)e"“ dx -KO Appendix 2B Fourier Transforms, Integrals, and Series 2B.1 2B.2 2B.3 2B.4 2B.5 213.6 2B.7 Introduction Transforms . . . . Infinite One-dimensional Transforms .
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If this viewpoint be adopted, the methods of interpretation and evaluation of em' to be presented below will be found consistent with its definition. Alternately, if the definition of e'"' be taken as that given in Sec.
If this viewpoint be adopted, the methods of interpretation and evaluation of em' to be presented below will be found consistent with its definition. Alternately, if the definition of e'"' be taken as that given in Sec.
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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 ...
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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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