Some Mathematical Methods of PhysicsCourier Corporation, 2014 M03 5 - 320 páginas This 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
... Variable . . . . . . . . . 32 2.8 The Steady-state Solution . . . . . . . . 34 2.9 The Inhomogeneous Problem . . . . . . . 35 Chapter 3 The Evaluation of a Function of a Matrix for an Arbitrary Matrix 38 3.1 Introduction ...
... Variable . . . . . . . . . 32 2.8 The Steady-state Solution . . . . . . . . 34 2.9 The Inhomogeneous Problem . . . . . . . 35 Chapter 3 The Evaluation of a Function of a Matrix for an Arbitrary Matrix 38 3.1 Introduction ...
Página x
... Variables . 1C.1 1C.2 1C3 1C.4 1C.5 Analytic Functions . . . . . The Cauchy Integral Theorem and Corollary Singularities . . . . . . Cauchy's Integral Formula . The Theorem of Residues . 184 185 190 192 201 201 202 203 204 205 206 207 ...
... Variables . 1C.1 1C.2 1C3 1C.4 1C.5 Analytic Functions . . . . . The Cauchy Integral Theorem and Corollary Singularities . . . . . . Cauchy's Integral Formula . The Theorem of Residues . 184 185 190 192 201 201 202 203 204 205 206 207 ...
Página 3
... variables (the coordinates of the physical system) and one independent variable (the time). Part One is concerned solely with the solution of such systems of equations for prescribed initial conditions. Several physical problems and the ...
... variables (the coordinates of the physical system) and one independent variable (the time). Part One is concerned solely with the solution of such systems of equations for prescribed initial conditions. Several physical problems and the ...
Página 4
... of the two new dependent variables x3 and x4. mic1 = x3 mic2 = x4 *3 = ko(x2 _ x1) _ kxl 5'4 = ko(X1 — x2) '* kxz um A more fundamental change in the form of the equations. 4 SYSTEMS WITH A FINITE NUMBER OF DEGREES OF FREEDOM.
... of the two new dependent variables x3 and x4. mic1 = x3 mic2 = x4 *3 = ko(x2 _ x1) _ kxl 5'4 = ko(X1 — x2) '* kxz um A more fundamental change in the form of the equations. 4 SYSTEMS WITH A FINITE NUMBER OF DEGREES OF FREEDOM.
Página 5
... variables do not change with time ? To find this steady-state solution of (1.7) one sets it = j» = 0 and thus has to solve 0 I <1» To find the steady-state solution of (1.8) one need merely solve kxl : k0(x2 — x1) + F! (L10) kxz : ko(x1 ...
... variables do not change with time ? To find this steady-state solution of (1.7) one sets it = j» = 0 and thus has to solve 0 I <1» To find the steady-state solution of (1.8) one need merely solve kxl : k0(x2 — x1) + F! (L10) kxz : ko(x1 ...
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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