New Quantum-Mechanical Representation

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Abstract
The superlattice representation is described. This representation provides occupation probabilities which form a well-defined non-negative definite analog of the phase space density. The superlattice basis functions are orthonormal wave packets characterized in general by three parameters: a band index, a wave vector, and a superlattice position vector. The crystal momentum and position are automatically coarse-grained so as to satisfy the Heisenberg uncertainty principle. The Bloch and Wannier representations are special cases of the superlattice representation for particular choices of the superlattice parameter. Joint functions of position and momentum, such as the local current density, can be represented as the expectation value of Hermitian operators through the use of this representation.

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