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 v
... applied physics, such as quantum mechanics, acoustics, electromagnetic theory, and reactor physics. In an attempt to develop this background in one coherent manner, rather than have it appear in bits and pieces in various courses, one ...
... applied physics, such as quantum mechanics, acoustics, electromagnetic theory, and reactor physics. In an attempt to develop this background in one coherent manner, rather than have it appear in bits and pieces in various courses, one ...
Página 5
... applied to the mass. In this case (1.5) becomes mi = y y = ~kx + F(t) (1'7) Similarly, if in the system sketched in Fig. 1.2 a force F1(t) is applied to mass 1 and a force F 2(t) is applied to mass 2, the equations of motion become, in ...
... applied to the mass. In this case (1.5) becomes mi = y y = ~kx + F(t) (1'7) Similarly, if in the system sketched in Fig. 1.2 a force F1(t) is applied to mass 1 and a force F 2(t) is applied to mass 2, the equations of motion become, in ...
Página 23
... applied to such f for which convergent power series do not exist, provided that the right side of (2.8) is meaningful. 2.3 Superposition The problem under consideration is the evaluation of the solution (2.4) of the differential ...
... applied to such f for which convergent power series do not exist, provided that the right side of (2.8) is meaningful. 2.3 Superposition The problem under consideration is the evaluation of the solution (2.4) of the differential ...
Página 26
... applied to the function f(A) = A, there results the remarkable relation A = sAs'l (2.22) in which A has been written in terms of the diagonal matrix of its eigenvalues.2 Thus, A is said to be diagonalizable. This definition implies that ...
... applied to the function f(A) = A, there results the remarkable relation A = sAs'l (2.22) in which A has been written in terms of the diagonal matrix of its eigenvalues.2 Thus, A is said to be diagonalizable. This definition implies that ...
Página 28
... applied by showing that a1 vanishes. To do this, it is assumed that 1' runs from 1 to m. Then, to eliminate the term in the sum (2.25) which contains 42,, (2.25) is multiplied from the left by A — 12. This multiplies each term in the ...
... applied by showing that a1 vanishes. To do this, it is assumed that 1' runs from 1 to m. Then, to eliminate the term in the sum (2.25) which contains 42,, (2.25) is multiplied from the left by A — 12. This multiplies each term in the ...
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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