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
... first sentence of Sec. 1.] appear the words “are linear, have a finite number of degrees of freedom, and have properties independent of time.” The limitations implied by these words are readily interpreted with the aid of Eqs. (1.16) ...
... first sentence of Sec. 1.] appear the words “are linear, have a finite number of degrees of freedom, and have properties independent of time.” The limitations implied by these words are readily interpreted with the aid of Eqs. (1.16) ...
Página 8
... first glance it may seem that this apparent simplicity merely hides the truth. However, it will be found that the solution of (1.19) which would hold if x and m were l X 1 matrices (scalars) also holds if x and m are matrices. That is ...
... first glance it may seem that this apparent simplicity merely hides the truth. However, it will be found that the solution of (1.19) which would hold if x and m were l X 1 matrices (scalars) also holds if x and m are matrices. That is ...
Página 10
... First, the equality of two matrices will be discussed. Two matrices may be equated only if each has the same number of columns and the same number of rows as the other. In this case, the matrices are equal if each element of one equals ...
... First, the equality of two matrices will be discussed. Two matrices may be equated only if each has the same number of columns and the same number of rows as the other. In this case, the matrices are equal if each element of one equals ...
Página 13
... first difference to be considered is the noncommutativity of matrix multiplication. That is, there are matrices p and m such that mp oé pm In fact, an example of such a pair of matrices is given by (1 °) I" 'I m 0 —1 p 1 0 This ...
... first difference to be considered is the noncommutativity of matrix multiplication. That is, there are matrices p and m such that mp oé pm In fact, an example of such a pair of matrices is given by (1 °) I" 'I m 0 —1 p 1 0 This ...
Página 16
... first be shown that there exists a q such that mq I I, second that there exists a p such that pm = I, and third that p = q. To find q such that mq = I, one need merely solve the equations for each of the n columns of q in turn. These ...
... first be shown that there exists a q such that mq I I, second that there exists a p such that pm = I, and third that p = q. To find q such that mq = I, one need merely solve the equations for each of the n columns of q in turn. These ...
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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