Z

z where v labels the quantum well eigenstates (energy ev), that is, the quantum well bound (ev < V0) and unbound states (ev > V0) and k± = (kx, ky). Since the \v, k±) basis is complete we may always expand the impurity wavefunction ^loc in the form lfoc> = E c(v,k±)\v,k±)

The Coulombic potential couples a given subband v, as well as a given vector k± with all others. The intersubband coupling (especially the one with the subbands of the quantum well continuum) is difficult to handle. In a quasi-two-dimensional situation we would like to set c(v, k±) = cVo(k±)8v vg, that is, to neglect intersubband coupling [67, 68]. This procedure is convenient as the impurity wavefunction displays a separable form:

The wavefunction p(p) is the solution of the two-dimensional Schrodinger equation p + P2 2m*

where Feff is the effective in-plane Coulombic potential,

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