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The Harmonic Oscillator
Orbital angular momentum and the spherical harmonics
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amplitude angles antilinear antilinear operator antisymmetrical antiunitary applying approximation atom basis vectors calculation classical coefficients collision commutation relations components condition conservation consider constant corresponding cross section deduce defined definition degeneracy denote density Dirac Dirac equation eigenfunctions eigenvalue eigenvectors electrons energy equal expansion expression fermions field formula given gives half-integral Hamiltonian Hermitean identical identical particles independent infinitesimal rotation integral interaction invariant under rotation irreducible tensor operator ji j2 levels magnetic matrix elements momenta neutrons notation nucleons nucleus observables obtained orthogonal orthonormal parity particular permutation perturbation phase factor physical potential problem projector properties protons Quantum Mechanics quantum numbers representation represented right-hand side rotation operator satisfies scalar product scattering Schrodinger solution space spectrum spherical harmonics subspace suppose symmetrical theorem theory tion total angular momentum transformation transition unitary vector operator wave function