# An eigenvalue problem for a Fermi system and Lie algebras

An eigenvalue problem for a Fermi system and Lie algebras We study a Fermi Hamilton operator $$\hat{K}$$ K ^ which does not commute with the number operator $$\hat{N}$$ N ^ . The eigenvalue problem and the Schrödinger equation are solved. Entanglement is also discussed. Furthermore, the Lie algebra generated by the two terms of the Hamilton operator is derived, and the Lie algebra generated by the Hamilton operator and the number operator is also classified. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# An eigenvalue problem for a Fermi system and Lie algebras

, Volume 13 (2) – Oct 10, 2013
10 pages

/lp/springer_journal/an-eigenvalue-problem-for-a-fermi-system-and-lie-algebras-IiNecltzw0
Publisher
Springer US
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-013-0650-5
Publisher site
See Article on Publisher Site

### Abstract

We study a Fermi Hamilton operator $$\hat{K}$$ K ^ which does not commute with the number operator $$\hat{N}$$ N ^ . The eigenvalue problem and the Schrödinger equation are solved. Entanglement is also discussed. Furthermore, the Lie algebra generated by the two terms of the Hamilton operator is derived, and the Lie algebra generated by the Hamilton operator and the number operator is also classified.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Oct 10, 2013

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