Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 52
... base vectors . They define the coordinate system , or basis , in which x , y , z are the coordinates of the particle . Note that the base vectors i , j , k are linearly independent : If r = 0 , then x = y = z = 0. Any vector in three ...
... base vectors . They define the coordinate system , or basis , in which x , y , z are the coordinates of the particle . Note that the base vectors i , j , k are linearly independent : If r = 0 , then x = y = z = 0. Any vector in three ...
Página 67
... base ket vectors , or simply base kets . The base vectors in the dual space , ut , are called base bra vectors , or base bras , and are denoted by < i ] , the mirror image of the symbol for the base kets . Using the convention that a ...
... base ket vectors , or simply base kets . The base vectors in the dual space , ut , are called base bra vectors , or base bras , and are denoted by < i ] , the mirror image of the symbol for the base kets . Using the convention that a ...
Página 68
... base vectors in different bases are distinguished by use of different letters ( e.g. , u¿ , V1 , w1 , etc. ) only different indices are used in the Dirac notation . The n different base vectors which constitute a basis are denoted by ...
... base vectors in different bases are distinguished by use of different letters ( e.g. , u¿ , V1 , w1 , etc. ) only different indices are used in the Dirac notation . The n different base vectors which constitute a basis are denoted by ...
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