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Inducing normally forbidden transitions within the conduction band of GaAs quantum wells
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12.The sum of the QWEST oscillator strengths from the first quantum state is about 17.4. The transitions to the lower valence and other bands contribute about —16 to the oscillator strength so the sum is unity. Note, multiplication of the QWEST oscillator stengths by to obtain unity is not correct, one must sum all transitions, including interband. The use of an effective mass Hamiltonian for the conduction band also leads to a sum rule of for the QWESTs alone, but this approximation is inadequate for a quantitative sum rule as it improperly assumes the reduced envelope wave functions have the usual boundary conditions, and neglects nonuniform effective masses, nonparabolicity of energy bands, interactions with other bands, and other real crystal effects.
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