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 F ( B ) = Σ c „ B " where n is a positive integer and the c , 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 F ( B ) = Σ c „ B " where n is a positive integer and the c , are numbers . 12. Show that if A is any ...
Página 133
... commute with the Laplacian operator , i.e. , = --- = It is convenient to introduce the operator L = i a до - - x a ду 0 y ax ( 10.22 ) which also commutes with the Laplacian . Equations ( 10.19 ) , ( 10.20 ) , and ( 10.21 ) may then be ...
... commute with the Laplacian operator , i.e. , = --- = It is convenient to introduce the operator L = i a до - - x a ду 0 y ax ( 10.22 ) which also commutes with the Laplacian . Equations ( 10.19 ) , ( 10.20 ) , and ( 10.21 ) may then be ...
Página 148
... commute with V2 , r2 , L. , L „ , and L. 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 L. 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
34 | 12 |
Solution for Diagonalizable Matrices | 21 |
The Evaluation of a Function of a Matrix for an Arbitrary Matrix | 38 |
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approximation arbitrary ax² basis Bessel functions boundary conditions Chap coefficients column consider constant continuous systems contour coordinates corresponding cylindrical functions d²/dx² defined definition denoted determinant diagonal differential equation Dirac notation domain eigencolumns eigenfunctions eigenvectors elements evaluate expansion F₁ finite number follows formula Fourier given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral inverse Laplacian linear operator linearly independent lowest eigenvalue Mathematical matrix McGraw-Hill Book Company method multiplication nonsingular normal number of degrees obtained orthonormality conditions Physics problem relations representation result Ritz method scattering sinh solution solve spherical spherical harmonics string Substitution theorem transform trial functions vanish variable vector space Verify w₁ wave write written x₁ Y₁ yields York zero ηπχ ди ду дх