Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 216
... trial functions f ( a , ß , y , ... ) depending on the parameters α , ẞ , y , .... Then λ is in turn a function of these parameters , i.e. , λ = λ ( α , ẞ , y , ... ) . The best available estimate of λ , for the given 2 class of trial ...
... trial functions f ( a , ß , y , ... ) depending on the parameters α , ẞ , y , .... Then λ is in turn a function of these parameters , i.e. , λ = λ ( α , ẞ , y , ... ) . The best available estimate of λ , for the given 2 class of trial ...
Página 217
... trial functions 1 , instead of in the original space in which the operator was defined , and has found the lowest value of 2 in this subspace . If the set of trial functions ; is not orthonormal , one can still use the result ( 15.22 ) ...
... trial functions 1 , instead of in the original space in which the operator was defined , and has found the lowest value of 2 in this subspace . If the set of trial functions ; is not orthonormal , one can still use the result ( 15.22 ) ...
Página 220
... functions , by 4. = Σaio Pi The set of trial functions 4 , are equivalent to the set ø , and will lead to the same roots . Now consider , with n < N , the trial functions Since n f = Σ.Φ. σ = 1 ( 15.30 ) Ho + H & 2 = Σã¡œŸi * Hа ̧ ...
... functions , by 4. = Σaio Pi The set of trial functions 4 , are equivalent to the set ø , and will lead to the same roots . Now consider , with n < N , the trial functions Since n f = Σ.Φ. σ = 1 ( 15.30 ) Ho + H & 2 = Σã¡œŸi * Hа ̧ ...
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