Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 126
... wave in a finite string as a superposition of waves traveling to the right and to the left . Thus the wave traveling to the right ( increasing x ) may be written as · A + = y ( ) ct , 0 ) 1 x - ct 2c a ( u , 0 ) du and the wave ...
... wave in a finite string as a superposition of waves traveling to the right and to the left . Thus the wave traveling to the right ( increasing x ) may be written as · A + = y ( ) ct , 0 ) 1 x - ct 2c a ( u , 0 ) du and the wave ...
Página 176
... waves outward from a given source . Let c represent the velocity of propagation . Then , the amplitude of the wave ( r , t ) at the point r at time t satisfies both the inhomogeneous wave equation 22 at2 Y ( r , t ) = c2S ( r , t ) ...
... waves outward from a given source . Let c represent the velocity of propagation . Then , the amplitude of the wave ( r , t ) at the point r at time t satisfies both the inhomogeneous wave equation 22 at2 Y ( r , t ) = c2S ( r , t ) ...
Página 185
... wave of ( 13.39 ) has a density of | incl2 = leikz | 2 = 1 , so that it corresponds to an incident current density of clinc2 = c . According to ( 13.40 ) , the outgoing wave at large r corresponds to a radial outward current density of ...
... wave of ( 13.39 ) has a density of | incl2 = leikz | 2 = 1 , so that it corresponds to an incident current density of clinc2 = c . According to ( 13.40 ) , the outgoing wave at large r corresponds to a radial outward current density of ...
Contenido
Solution for Diagonalizable Matrices | 21 |
12 | 37 |
Vector Spaces and Linear Operators | 50 |
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analytic approximate arbitrary asymptotic ax² Bessel function boundary conditions chap coefficients consider constant contour coordinates corresponding cylindrical functions d₁ d²/dx² defined denotes determinant diagonal differential equation Dirac notation ei(p eigen eigencolumn eigenfunctions eigenvalue equation eigenvalue problem eigenvector eikr element evaluate expansion finite number follows Fourier integral theorem function f(x given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral representation integrand inverse Laplacian linear lowest eigenvalue matrix method multiplication notation obtained operator orthonormality conditions perturbation plane relations result Ritz method row or column saddle point saddle-point method satisfy the orthonormality scattering sinh solution solve spherical spherical harmonics substitution transformation functions trial functions vanish variable vector vector space verified wave written yields zero ηπχ πρ ди ду дх