Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 20
... commute with one another . 11. Show that if a matrix A commutes with another matrix B , then A commutes with any matrix of the form C F ( B ) = Σc2B " n where n is a positive integer and the c2 are numbers . 12. Show that if A is any ...
... commute with one another . 11. Show that if a matrix A commutes with another matrix B , then A commutes with any matrix of the form C F ( B ) = Σc2B " n where n is a positive integer and the c2 are numbers . 12. Show that if A is any ...
Página 133
... commute with the Laplacian operator , i.e. , [ Ə ± ‚ V2 ] = Ə ± √2 — ▽ 2 Ə ± − 0 It is convenient to introduce the operator L = ә -i 20 = - ә ду - - y ax ( 10.22 ) which also commutes with the Laplacian . Equations ( 10.19 ) ...
... commute with the Laplacian operator , i.e. , [ Ə ± ‚ V2 ] = Ə ± √2 — ▽ 2 Ə ± − 0 It is convenient to introduce the operator L = ә -i 20 = - ә ду - - y ax ( 10.22 ) which also commutes with the Laplacian . Equations ( 10.19 ) ...
Página 148
... commute with V2 , r2 , L , L , and L2 . It , therefore , seems plausible that a complete set of commuting observ- ables might consist of V2 , L2 , and L ,. Assuming that such is the case , let us look for simultaneous eigenfunctions of ...
... commute with V2 , r2 , L , L , and L2 . It , therefore , seems plausible that a complete set of commuting observ- ables might consist of V2 , L2 , and L ,. Assuming that such is the case , let us look for simultaneous eigenfunctions of ...
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