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 5
... solving the equations of motion suggests itself : What solutions exist in which the dependent variables do not change with ... solve kxl : k0(x2 — x1) + F! (L10) kxz : ko(x1 _ x2) + F2 1.2 Standardization of Notation In order to focus ...
... solving the equations of motion suggests itself : What solutions exist in which the dependent variables do not change with ... solve kxl : k0(x2 — x1) + F! (L10) kxz : ko(x1 _ x2) + F2 1.2 Standardization of Notation In order to focus ...
Página 8
... solve (1.20). It may be argued that (1.21) is, in conjunction with (1.19), no more than a definition of e'"'. If this viewpoint be adopted, the methods of interpretation and evaluation of em' to be presented below will be found ...
... solve (1.20). It may be argued that (1.21) is, in conjunction with (1.19), no more than a definition of e'"'. If this viewpoint be adopted, the methods of interpretation and evaluation of em' to be presented below will be found ...
Página 16
... solve the equations for each of the n columns of q in turn. These are mqa' : (54' (1-42) for the ith column of q. Written out, they become 2 miqui = 6n ,_. As follows directly from property 2, these equations have a unique solution for ...
... solve the equations for each of the n columns of q in turn. These are mqa' : (54' (1-42) for the ith column of q. Written out, they become 2 miqui = 6n ,_. As follows directly from property 2, these equations have a unique solution for ...
Página 17
... solving n equations in n unknowns. Thus, consider the equation mx : y (1.46) For nonsingular m, a solution x exists for all y. For singular m, clearly a solution x exists for some y—i.e., for those y which may be written as a linear ...
... solving n equations in n unknowns. Thus, consider the equation mx : y (1.46) For nonsingular m, a solution x exists for all y. For singular m, clearly a solution x exists for some y—i.e., for those y which may be written as a linear ...
Página 18
... Solve Eqs. (1.10) for x1 and x2. 2. Given the values fl, g, in the table, evaluate 4 4 4 4 2 ft 2 8t fiz 8i i=1 i=1 i=1 t=1 4 2 4 4 4 210} + 3") 21. igi Zl-Ii'gii'l glfnqgi i | 1 2 3 4 5 f,- ' 1 1.5 2.1 2.8 3.6 g,- 0.7 0.9 1.2 1.6 2.1 0 ...
... Solve Eqs. (1.10) for x1 and x2. 2. Given the values fl, g, in the table, evaluate 4 4 4 4 2 ft 2 8t fiz 8i i=1 i=1 i=1 t=1 4 2 4 4 4 210} + 3") 21. igi Zl-Ii'gii'l glfnqgi i | 1 2 3 4 5 f,- ' 1 1.5 2.1 2.8 3.6 g,- 0.7 0.9 1.2 1.6 2.1 0 ...
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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