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 28
... multiplication with A — 13. This process is continued until all terms in the sum (2.25) have been annihilated except the first (the last factor needed is clearly A — 2,"). At this time, (2.25) has become (41 '" 4901 _ 3X41 _' 44) ...
... multiplication with A — 13. This process is continued until all terms in the sum (2.25) have been annihilated except the first (the last factor needed is clearly A — 2,"). At this time, (2.25) has become (41 '" 4901 _ 3X41 _' 44) ...
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... Multiplication of (3.17) by e-Zt dt and integration from 0 to 00 yields ZU—u(0)=AU+F or (z - A)U(Z) = “(0) + F(Z) (3.20) Once U(Z) is determined from (3.20), use of the inversion formula u(t) = eZ'U(Z) dZ ' (3.21) 21ri yields u(t). As ...
... Multiplication of (3.17) by e-Zt dt and integration from 0 to 00 yields ZU—u(0)=AU+F or (z - A)U(Z) = “(0) + F(Z) (3.20) Once U(Z) is determined from (3.20), use of the inversion formula u(t) = eZ'U(Z) dZ ' (3.21) 21ri yields u(t). As ...
Página 52
... multiplication of vectors known as scalar multiplication, defined by the relations i-j=j'i=j-k=k-j=k-i=i-k=0 4.5 ~1=j~j=k~k=1 ( ) and to require that scalar multiplication of vectors obey the distributive law in multiplication. Thus r2 ...
... multiplication of vectors known as scalar multiplication, defined by the relations i-j=j'i=j-k=k-j=k-i=i-k=0 4.5 ~1=j~j=k~k=1 ( ) and to require that scalar multiplication of vectors obey the distributive law in multiplication. Thus r2 ...
Página 53
... multiplication of complex vectors in an n-dimensional vector space. If (4.8) holds, the u,+ and u,- form a bi-orthonormal basis. The relation (4.8) isknown as the bi-orthonormality condition. 1 A vector space is, by definition, n ...
... multiplication of complex vectors in an n-dimensional vector space. If (4.8) holds, the u,+ and u,- form a bi-orthonormal basis. The relation (4.8) isknown as the bi-orthonormality condition. 1 A vector space is, by definition, n ...
Página 54
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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