Boundary conditions on current carrying states and the implications for observations of bloch oscillations
Abstract
The problem of the precise form (together with the associated boundary conditions) of a onedimensional hamiltonian describing a particle of variable mass is addressed. It is shown that although hermiticity may be a necessary condition, it is not sufficient to specify uniquely the hamiltonian. In particular one form of the latter that is widely employed in the literature is shown to lead to a violation of the Heisenberg Uncertainty Principle. However imposition of the additional demand that any singular terms arising from the kinetic energy can be transformed away does lead to a unique specification of the hamiltonian. Finally the implications of the latter with regard to the standard probability interpretation of the wavefunction and for the observation of Bloch oscillations in quantum well structures is described.
 Publication:

Superlattices and Microstructures
 Pub Date:
 March 1994
 DOI:
 10.1006/spmi.1994.1040
 Bibcode:
 1994SuMi...15..199H