Phys. Rev. A 79, 014101 (2009) [4 pages]Hamiltonians generating optimal-speed evolutionsReceived 18 April 2008; published 6 January 2009 We present a simple derivation of the formula for the Hamiltonian operator(s) that achieve the fastest possible unitary evolution between given initial and final states. We discuss how this formula is modified in pseudo-Hermitian quantum mechanics and provide an explicit expression for the most general optimal-speed quasi-Hermitian Hamiltonian. Our approach allows for an explicit description of the metric (inner product) dependence of the lower bound on the travel time and the universality (metric independence) of the upper bound on the speed of unitary evolutions. © 2009 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevA.79.014101
DOI:
10.1103/PhysRevA.79.014101
PACS:
03.65.Xp, 03.67.Lx, 02.30.Yy, 02.40.−k
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