【Abstract】 We present a method for calculating collective excitation spectrum in semiconductor superlattices with a overlap of wavefunctions between adja- cent layers, in analogy with Feynman’s theory of helium and MacDo-nald’s approach in the Fractional Quantum Hall effect. The essential ideal is to divide the density operator ρk = ∑iexp(ik·ri) into two parts, ρkintraand ρkinter, corresponding to the contributions from the oscillations withinlayers and between adjacent layers, respectively, and then to write the variational density wave state aswhere lψo>is the ground state, from which we can obtain the equation of collective excitations. As Yang et al., first pointed out besides the usual excitations, there exists a new kind of mode originating from the tunnelling between adjacent layers. The advantage of the method is to avoid some complex calculations necessary to Yang’s Green Function approach. Its validity and comparison with experiments are also discussed.更多还原