energy can be expanded in powers of as where is the electron effective mass. It can be shown that it satisfies the equation Here the sum runs over all bands with . Therefore, the ratio of the free electron mass to its effective mass in a crystal can be considered as the oscillator strength for the transition of an electron from the quantum state at the bottom of the band into the same state. See also Atomic spectral line Sum rule in quantum mechanics Electronic band structure Einstein coefficients References Spectroscopy Atoms Crystals