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APS » Journals » Phys. Rev. D » Volume 32 » Issue 6
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Phys. Rev. D 32, 1476–1485 (1985)

Discrete-time quantum mechanics

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Carl M. Bender
Department of Physics, Washington University, St. Louis, Missouri 63130

Kimball A. Milton
Department of Physics, Oklahoma State University, Stillwater, Oklahoma 74078

David H. Sharp and L. M. Simmons, Jr.
Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545

Richard Stong
Department of Physics, Washington University, St. Louis, Missouri 63130

Received 18 January 1985; published in the issue dated 15 September 1985

The finite-element (collocation) method enables us to construct discrete time-lattice quantum systems that accurately approximate continuum quantum systems. The discrete quantum systems so generated are fully consistent quantum-mechanical systems in their own right. This paper gives a comprehensive treatment of such quantum systems. We examine various finite-element schemes, construct the effective lattice Hamiltonian, and calculate eigenvalues. Numerical results are extremely easy to obtain and are very accurate.

© 1985 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevD.32.1476
DOI:
10.1103/PhysRevD.32.1476
PACS:
11.15.Ha, 03.65.Ca
 
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