949 research outputs found
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
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