Momentum Dynamics of One Dimensional Quantum Walks

Details Momentum Dynamics of One Dimensional Quantum Walks Momentum Dynamics of One Dimensional Quantum Walks

2006-04-27

arxiv.org/abs/quant-ph/0604197v2

Physics

Quantum Physics

Typos corrected

Scientific paper

We derive the momentum space dynamic equations and state functions for one dimensional quantum walks by using linear systems and Lie group theory. The momentum space provides an analytic capability similar to that contributed by the z transform in discrete systems theory. The state functions at each time step are expressed as a simple sum of three Chebyshev polynomials. The functions provide an analytic expression for the development of the walks with time.

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