Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 109
... Similarly , the equation a f ( r , t ) = Lf ( r , t ) Ət a reduces to f ( r , t ) = D ( r ) f ( r , t ) Ət It is clear , therefore , that these conventional differential equations may be solved by the methods developed in the preceding ...
... Similarly , the equation a f ( r , t ) = Lf ( r , t ) Ət a reduces to f ( r , t ) = D ( r ) f ( r , t ) Ət It is clear , therefore , that these conventional differential equations may be solved by the methods developed in the preceding ...
Página 262
... Similarly lim F ( Rei ) eiR iRt cos 0- Rt sin 0 iReio do = 0 Finally | [ ~ * ~ * ~ F ( Re® ) e Rt com - Rt sin • ¡ Re1® d0 Ε 0 - Rt 0 iRei iRt cos 0- Rt sin F ( ReeRt = √ ̃ * ̃ ̄ | F ( Re ) \ e * ཀ ། Rt sine R do - Rt sin e ne R do | F ...
... Similarly lim F ( Rei ) eiR iRt cos 0- Rt sin 0 iReio do = 0 Finally | [ ~ * ~ * ~ F ( Re® ) e Rt com - Rt sin • ¡ Re1® d0 Ε 0 - Rt 0 iRei iRt cos 0- Rt sin F ( ReeRt = √ ̃ * ̃ ̄ | F ( Re ) \ e * ཀ ། Rt sine R do - Rt sin e ne R do | F ...
Página 267
... Similarly , comparison of ( 2B.2 ) with ( 2B.3 ) shows that < μl > = = < μ | 2 > < 2 | > ( 2B.7 ) ( 2B.8 ) The functions < 2 > and < μ > related by ( 2B.7 ) and ( 2B.8 ) are called transforms of one another ; e.g. , < ^ | > is a ...
... Similarly , comparison of ( 2B.2 ) with ( 2B.3 ) shows that < μl > = = < μ | 2 > < 2 | > ( 2B.7 ) ( 2B.8 ) The functions < 2 > and < μ > related by ( 2B.7 ) and ( 2B.8 ) are called transforms of one another ; e.g. , < ^ | > is a ...
Contenido
Perturbation of Eigenvalues | 14 |
The Laplacian v2 in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
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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