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
Solution for Diagonalizable Matrices | 21 |
12 | 37 |
Vector Spaces and Linear Operators | 50 |
Derechos de autor | |
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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