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
Perturbation of Eigenvalues | 14 |
The Laplacian v2 in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
Derechos de autor | |
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approximate arbitrary ax² basis Bessel function boundary conditions chap coefficients column consider constant continuous systems contour coordinates corresponding cylindrical functions d²/dx² defined denoted determinant diagonal differential equation Dirac notation domain eigen eigencolumns eigenfunctions eigenvalue equation eigenvector eikr evaluate expansion finite number follows Fourier given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral inverse Laplace transform Laplacian linear operator linearly independent lowest eigenvalue matrix membrane method multiplication nonsingular normal obtained orthonormality conditions plane problem procedure relations representation result satisfies the boundary scattering sinh solve spherical spherical harmonics string Substitution theorem trial functions vanish variable vector space Verify wave write written y₁ yields York zero ηπχ πο ποχ ди ду дх