Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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... Variational Estimates 15.1 Introduction 15.2 The Rayleigh Variational Principle 15.3 A Lower Bound 15.4 The Ritz Method 15.5 Higher Eigenvalues by the Ritz Method 15.6 Example of the Ritz Method Chapter 16 Iteration Procedures 16.1 ...
... Variational Estimates 15.1 Introduction 15.2 The Rayleigh Variational Principle 15.3 A Lower Bound 15.4 The Ritz Method 15.5 Higher Eigenvalues by the Ritz Method 15.6 Example of the Ritz Method Chapter 16 Iteration Procedures 16.1 ...
Página 213
... variational principle yields an upper limit to the lowest eigenvalue of a Hermitian operator . This result , while clearly very useful , is not as much so as might be desired . One would also like to obtain a lower bound to the ...
... variational principle yields an upper limit to the lowest eigenvalue of a Hermitian operator . This result , while clearly very useful , is not as much so as might be desired . One would also like to obtain a lower bound to the ...
Página 224
... variational principle to obtain an upper limit to the 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 ...
... variational principle to obtain an upper limit to the 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 ...
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