Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 209
... lowest eigenvalue of d2 dx2 + a2x + ax3 + bx1 ) q = λq λφ < x < + ∞∞ < x < + ∞∞ where p is finite everywhere and a and b are given constants . 2. Given the eigenvalue problem d2 doz y'n d02 = ληνη y ( 0 ) = у ( 2π ) = n2 , where n ...
... lowest eigenvalue of d2 dx2 + a2x + ax3 + bx1 ) q = λq λφ < x < + ∞∞ < x < + ∞∞ where p is finite everywhere and a and b are given constants . 2. Given the eigenvalue problem d2 doz y'n d02 = ληνη y ( 0 ) = у ( 2π ) = n2 , where n ...
Página 213
... lowest eigenvalue of the operator . In a like manner , it may be demonstrated that is not greater than the highest eigenvalue of H. As an example , consider the approximate evaluation of the lowest eigenvalue ( 21 = 2 ) of the vibrating ...
... lowest eigenvalue of the operator . In a like manner , it may be demonstrated that is not greater than the highest eigenvalue of H. As an example , consider the approximate evaluation of the lowest eigenvalue ( 21 = 2 ) of the vibrating ...
Página 224
... lowest eigenvalue of d2y d02 = - ( λ — € cos2 0 ) y y ( 0 ) = у ( 2π ) Minimize this upper limit . 4. Evaluate approximately the lowest eigenvalue of the vibrating- string problem d2y dx2 + λργ = 0 y ( 0 ) = y ( 1 ) = 0 ρ p = 1 for 0 ...
... lowest eigenvalue of d2y d02 = - ( λ — € cos2 0 ) y y ( 0 ) = у ( 2π ) Minimize this upper limit . 4. Evaluate approximately the lowest eigenvalue of the vibrating- string problem d2y dx2 + λργ = 0 y ( 0 ) = y ( 1 ) = 0 ρ p = 1 for 0 ...
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