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 viii
... Eigenvectors of a Linear Operator . 61 4.10 The Diagonalization of Normal Matrices . . . . 64 Chapter 5 The Dirac Notation 67 5.1 Introduction . . . 67 5.2 The Change of Basis . . . 68 5.3 Linear Operators in the Dirac Notation 69 5.4 ...
... Eigenvectors of a Linear Operator . 61 4.10 The Diagonalization of Normal Matrices . . . . 64 Chapter 5 The Dirac Notation 67 5.1 Introduction . . . 67 5.2 The Change of Basis . . . 68 5.3 Linear Operators in the Dirac Notation 69 5.4 ...
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... eigenvectors of A sufiices to enable the evaluation off(A) and the solution of the initial value problems earlier considered. It will now be shown that an arbitrary column u may be written as a linear combination of the eigencolumns of ...
... eigenvectors of A sufiices to enable the evaluation off(A) and the solution of the initial value problems earlier considered. It will now be shown that an arbitrary column u may be written as a linear combination of the eigencolumns of ...
Página 26
... eigenvectors form a complete. (0 0) 1 0 1 This is clearly not a new definition but follows from the result (2.16) applied to a diagonal matrix. Thus, for a diagonal matrix one may take 5 = I = .9“. With this value of s, (2.18) follows ...
... eigenvectors form a complete. (0 0) 1 0 1 This is clearly not a new definition but follows from the result (2.16) applied to a diagonal matrix. Thus, for a diagonal matrix one may take 5 = I = .9“. With this value of s, (2.18) follows ...
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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