Limited accuracy of conduction band effective mass equations for semiconductor quantum dots

Effective mass equations are the simplest models of carrier states in a semiconductor structures that reduce the complexity of a solid-state system to Schr\"odinger- or Pauli-like equations resempling those well known from quantum mechanics textbooks. Here we present a systematic derivation of a conduction-band effective mass equation for a self-assembled semiconductor quantum dot in a magnetic field from the 8-band kp theory. The derivation allows us to classify various forms of the effective mass equations in terms of a hierarchy of approximations. We assess the accuracy of the approximations in calculating selected spectral and spin-related characteristics. We indicate the importance of preserving the off-diagonal terms of the valence band Hamiltonian and argue that an effective mass theory cannot reach satisfactory accuracy without self-consistently including non-parabolicity corrections and renormalization of kp parameters. Quantitative comparison with the 8-band kp results supports the phenomenological Roth-Lax-Zwerdling formula for the g-factor in a nanostructure.Comment: Final versio

Squeezed States and Helmholtz Spectra

The 'classical interpretation' of the wave function psi(x) reveals an interesting operational aspect of the Helmholtz spectra. It is shown that the traditional Sturm-Liouville problem contains the simplest key to predict the squeezing effect for charged particle states.Comment: 10 pages, Latex, 3 gzip-compressed figures in figh.tar.g