The hydrogen atom as an entangled electron-proton system

American Journal of Physics

Volumn 66, Issue 10, 1998, Pages 881-886

  Tommasini, Paolo ^a   Timmermans, Eddy ^a   De Toledo Piza, A F R ^b  

^a HARVARD SMITHSONIAN CENTER FOR ASTROPHYSICS   (United States)

^b UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032376597     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.18977     Document Type: Article

References (18)

1. J. von Neumann, Mathematical Foundations of Quantum Mechanics (Princeton U.P., Princeton, 1955).
2. E. Schrödinger, "Probability Relations Between Separate Systems," Proc. Cambridge Philos. Soc., 31 555-563 (1935); "Probability Relations Between Separate Systems," 32, 446-452 (1936).
3. E. Schrödinger, "Probability Relations Between Separate Systems," Proc. Cambridge Philos. Soc., 31 555-563 (1935); "Probability Relations Between Separate Systems," 32, 446-452 (1936).
4. Roland Omnès, The Interpretation of Quantum Mechanics (Princeton U.P., Princeton, NJ, 1994).
5. L. D. Landau and E. M. Lifschitz, Quantum Mechanics, Non-relativistic Theory (Addision-Wesley, Reading, MA, 1965), 2nd ed. The density operator was called "statistical operator" by von Neumann in Ref. 1.
6. U. Fano, "Description of States in Quantum Mechanics by Density Matrix and Operator Techniques," Revs. Mod. Phys. 29, 74-93 (1957).
7. L. Davidovich, M. Brune, J. M. Raymond, and S. Haroche, "Mesoscopic Quantum coherences in cavity QED: Preparation and Decoherence Monitoring Schemes," Phys. Rev A 53, 1295-1309 (1996); M. Brune, E. Hagley, J. Dreyer, X. Maître, A. Maali, C. E. Wunderlich, J. M. Raymond, and S. Haroche, "Observing the Progressive Decoherence of the 'Meter' in a Quantum Measurement," Phys. Rev. Lett. 77, 4887-4890 (1996).
8. L. Davidovich, M. Brune, J. M. Raymond, and S. Haroche, "Mesoscopic Quantum coherences in cavity QED: Preparation and Decoherence Monitoring Schemes," Phys. Rev A 53, 1295-1309 (1996); M. Brune, E. Hagley, J. Dreyer, X. Maître, A. Maali, C. E. Wunderlich, J. M. Raymond, and S. Haroche, "Observing the Progressive Decoherence of the 'Meter' in a Quantum Measurement," Phys. Rev. Lett. 77, 4887-4890 (1996).
9. E. Schmidt, "Zur Theorie Derlinearen und Nichtlinearen Integralgleichungen," Math. Annalen 63, 433-476 (1906).
10. M. C. Nemes and A. F. R. de Toledo Piza, "Effective Dynamics of Quantum Subsystems," Physica A 137, 367-388 (1986).
11. A. Ekert and P. L. Knight, "Entangled Quantum Systems and the Schmidt Decomposition," Am. J. Phys. 63, 415-423 (1995).
12. 2, where N is the number of nonvanishing eigenvalues λ, and is thus clearly related to the linear entropy. The essential ingredient in all these measures is a nonlinear dependence on ρ that makes it sensitive to the lack of idempotency of the density operator.
13. 2, where N is the number of nonvanishing eigenvalues λ, and is thus clearly related to the linear entropy. The essential ingredient in all these measures is a nonlinear dependence on ρ that makes it sensitive to the lack of idempotency of the density operator.
14. 2, where N is the number of nonvanishing eigenvalues λ, and is thus clearly related to the linear entropy. The essential ingredient in all these measures is a nonlinear dependence on ρ that makes it sensitive to the lack of idempotency of the density operator.
15. 2, where N is the number of nonvanishing eigenvalues λ, and is thus clearly related to the linear entropy. The essential ingredient in all these measures is a nonlinear dependence on ρ that makes it sensitive to the lack of idempotency of the density operator.
16. 2, where N is the number of nonvanishing eigenvalues λ, and is thus clearly related to the linear entropy. The essential ingredient in all these measures is a nonlinear dependence on ρ that makes it sensitive to the lack of idempotency of the density operator.
17. 2, where N is the number of nonvanishing eigenvalues λ, and is thus clearly related to the linear entropy. The essential ingredient in all these measures is a nonlinear dependence on ρ that makes it sensitive to the lack of idempotency of the density operator.
18. 2, in Ref. 10. In view of the close relationship between ρ̄(k) and the momentum distribution f(p), we choose to calculate the standard deviation of f(p) as the width of the momentum distribution in p space.