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 6
... zero time. Equations (1.1), (1.2), (1.5), and (1.6), when written in the form of (1.1 1), become _ __1_ E_ RCE (1.12) NI:T-11\r,+01v2+01va T1 . 1 -1 N z -—-N (—)N ON 1.13 2 T1 1+ T2 2+ 3 ( ) N,=01v,+l1~12+01v3 T2 it I 0x + ly m (1.14) ...
... zero time. Equations (1.1), (1.2), (1.5), and (1.6), when written in the form of (1.1 1), become _ __1_ E_ RCE (1.12) NI:T-11\r,+01v2+01va T1 . 1 -1 N z -—-N (—)N ON 1.13 2 T1 1+ T2 2+ 3 ( ) N,=01v,+l1~12+01v3 T2 it I 0x + ly m (1.14) ...
Página 7
... 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 the words “are linear, have a finite number of degrees ...
... 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 the words “are linear, have a finite number of degrees ...
Página 11
... zero is a zero matrix. Zero matrices have the expected properties 0+m:m OmImOZO In (1.32) the symbol 0 must indicate a zero matrix with the appropriate number of rows and of columns so that the operations are defined. In particular, in ...
... zero is a zero matrix. Zero matrices have the expected properties 0+m:m OmImOZO In (1.32) the symbol 0 must indicate a zero matrix with the appropriate number of rows and of columns so that the operations are defined. In particular, in ...
Página 12
... zero. That is Ii,- = 6,, (1.34) where the symbol 6,,- is the Kronecker delta symbol and is defined by the following relations 6,, = 1 6,, = 0 for 1' 7i j The importance of the Kronecker delta arises from (1.34) and from the ...
... zero. That is Ii,- = 6,, (1.34) where the symbol 6,,- is the Kronecker delta symbol and is defined by the following relations 6,, = 1 6,, = 0 for 1' 7i j The importance of the Kronecker delta arises from (1.34) and from the ...
Página 13
... zero: the product of two nonzero numbers is not zero; the same factor may be canceled from both sides of an equation; every number (except zero) has an inverse. In the case of matrices, there is a class of matrices which are nonzero and ...
... zero: the product of two nonzero numbers is not zero; the same factor may be canceled from both sides of an equation; every number (except zero) has an inverse. In the case of matrices, there is a class of matrices which are nonzero and ...
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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