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 7
... obtained from (1.16) by setting all the at, equal to zero and writing F, in place of F ,(t). These problems are again specified by n2 quantities m,,-, but require in addition the n numbers F,. In the first sentence of Sec. 1.] appear ...
... obtained from (1.16) by setting all the at, equal to zero and writing F, in place of F ,(t). These problems are again specified by n2 quantities m,,-, but require in addition the n numbers F,. In the first sentence of Sec. 1.] appear ...
Página 10
... 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 summation index and once with k as the summation index in order to obtain the ...
... 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 summation index and once with k as the summation index in order to obtain the ...
Página 11
Gerald Goertzel, Nunzio Tralli. time-dependent elements is obtained by replacing each element of the matrix with its time derivative. Thus. (Lm). :41”. d1 1; dl. (a). Zadt. i dt The product of two matrices is a somewhat complicated concept ...
Gerald Goertzel, Nunzio Tralli. time-dependent elements is obtained by replacing each element of the matrix with its time derivative. Thus. (Lm). :41”. d1 1; dl. (a). Zadt. i dt The product of two matrices is a somewhat complicated concept ...
Página 12
... obtaining the if element of the matrix product mp, where m and p are any two matrices such that the number of columns of m equals the number of rows of p. In fact, the 1'] element of mp is obtained by multiplying the ith row of m into ...
... obtaining the if element of the matrix product mp, where m and p are any two matrices such that the number of columns of m equals the number of rows of p. In fact, the 1'] element of mp is obtained by multiplying the ith row of m into ...
Página 17
... obtain a better understanding of the problem of 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. ...
... obtain a better understanding of the problem of 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. ...
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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