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angular momentum apply approximation beam Bohr chapter classical mechanics coefficients column vector complete components consider constant coordinates correspondence principle degeneracy detector Dirac Dirac notation eigenfunctions eigenstates eigenvectors electric dipole electron spin emission energy levels energy spectrum equation of motion evaluate exactly example experiment fact frequency gives Hamiltonian Hence Hermitian conjugate Hermitian matrix hydrogen atom important integral last section linear combination magnetic field matrix elements mean value measurement molecule normal modes notation observable obtain operator orthogonal orthonormal parameters Pauli matrices perturbation photon physical plane-polarized polynomial position possible values potential energy predicted probability problem quantum mechanics quantum number quantum particle quantum system radiation recipe relation representation represented requirements result Rule satisfied scalar product Schrodinger equation Show simple harmonic oscillator simultaneously solution spectral lines spherically symmetric Stark effect statevectors stationary Stern-Gerlach Stern-Gerlach experiment theory transition trial function velocity wave wavefunction write Zeeman effect zero