Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 19
... Verify ( 1.45 ) . 8. Let Ɛ = 0 0 0 100 Evaluate ε2 , € 3 , ett . 9 0 1 0 9. Find the nth power of the square matrix M defined by α M = B ( abc ) = 10. Verify that AB BA if A and B FORMULATION OF THE PROBLEM AND DEVELOPMENT OF NOTATION 19.
... Verify ( 1.45 ) . 8. Let Ɛ = 0 0 0 100 Evaluate ε2 , € 3 , ett . 9 0 1 0 9. Find the nth power of the square matrix M defined by α M = B ( abc ) = 10. Verify that AB BA if A and B FORMULATION OF THE PROBLEM AND DEVELOPMENT OF NOTATION 19.
Página 20
... Verify the distributive law 15. Verify that ( M + N ) P = MP + NP ( AB ) T = BTAT 16. Show that if M = AAT , then M = MT and hence M is a symmetric matrix . 17. Show that a nonsquare matrix cannot have an inverse . 18. Verify that the ...
... Verify the distributive law 15. Verify that ( M + N ) P = MP + NP ( AB ) T = BTAT 16. Show that if M = AAT , then M = MT and hence M is a symmetric matrix . 17. Show that a nonsquare matrix cannot have an inverse . 18. Verify that the ...
Página 163
... Verify that the operators L , L ,, and L , satisfy the commutation rules ( 11.9 ) . 2. Verify that - L‚L + − L + L , = L + - - LL_ — L_L1 = −L_ = - 3. Given [ L ,, P ] = P , [ L ,, Q ] | Q , [ P , Q ] = 2L ,, [ La‚P ] = [ L2 , Q ] = 0 ...
... Verify that the operators L , L ,, and L , satisfy the commutation rules ( 11.9 ) . 2. Verify that - L‚L + − L + L , = L + - - LL_ — L_L1 = −L_ = - 3. Given [ L ,, P ] = P , [ L ,, Q ] | Q , [ P , Q ] = 2L ,, [ La‚P ] = [ L2 , Q ] = 0 ...
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