Some mathematical methods of physics

approximation arbitrary base vectors basis Bessel functions boundary conditions Chap chapter coefficients column commute complete consider constant continuous systems contour corresponding cylindrical functions defined definition denoted determinant diagonal differential equation Dirac notation domain eigen eigencolumns eigenfunctions eigenvalue equation eigenvectors elements equations of motion evaluate example expansion finite number follows formal solution formula Fourier given Green's function Hence Hermitian matrix Hermitian operator infinite inverse Laplace transform Laplacian linear operator linearly independent lowest eigenvalue Mathematical matrix McGraw-Hill Book Company membrane method multiplication nonsingular normal normal matrix Note number of degrees obtained orthonormality condition perturbation Physics plane procedure relations representation result Ritz method saddle point satisfies the boundary scattering sinh solve spherical harmonics Substitution trial functions vanish variable vector space Verify wave write written yields York zero