Accession Number:

AD0261922

Title:

ON THE SUPERPOSITION OF PERIODIC POTENTIALS AND HOMOGENEOUS FIELDS

Descriptive Note:

Corporate Author:

OREGON UNIV EUGENE

Personal Author(s):

Report Date:

1960-01-01

Pagination or Media Count:

1.0

Abstract:

IN CONNECTION WITH EARLIER WORK Phys. Rev. 117432, 1960, wave functions are constructed for a superposition of a periodic electric potential and a uniform magnetic field. The wave functions are not themselves solutions of the Schroedinger equation, but yield the traditional effective hamiltonan for this problem. Contrary to the electric field case the manifold of states linked by the band index does not form a Bloch band the reason is that the cellular transforms of the Bloch-like functions are modified by the Peierls phase. At present, the derivation of these results is in closed form, but justifiable only to all powers of the magnetic field. This was also the case for the previous electric derivation. The limitation may not be genuine. The second half of the paper does in fact prove directly the existence of closed Bloch bands in the presence of a homogeneous electric field the case of free electrons is given as an example. One expects from this that the new results for the magnetic field are at least in part also independent of the power series method used for their justification. Author

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Distribution Statement:

APPROVED FOR PUBLIC RELEASE