ESTONIAN ACADEMY
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eesti teaduste
akadeemia kirjastus
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proceedings
of the estonian academy of sciences
ISSN 1736-7530 (Electronic)
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A global, dynamical formulation of quantum confined systems; pp. 290–293

Full article in PDF format | doi: 10.3176/proc.2010.4.06

Authors
Nuno C. Dias, João N. Prata

Abstract
A brief review of some recent results on the global self-adjoint formulation of systems with boundaries is presented. We concentrate on the 1-dimensional case and obtain a dynamical formulation of quantum confinement.
References

  1. Garbaczewski, P. and Karwowski, W. Impenetrable barriers and canonical quantization. Am. J. Phys., 2004, 72, 924–933.
doi:10.1119/1.1688784

  2. Isham, C. Topological and global aspects of quantum theory. In Relativity, Groups and Topology: No. 2: Summer School Proceedings (Les Houches Summer School Proceedings) (DeWitt, B. S. and Stora, R., eds). Elsevier, 1984, 1059–1290.

  3. Bonneau, G., Faraut, J., and Valent, G. Self-adjoint extensions of operators and the teaching of quantum mechanics. Am. J. Phys., 2001, 69, 322–331.
doi:10.1119/1.1328351

  4. Dias, N. C. and Prata, J. N. Wigner functions with boundaries. J. Math. Phys., 2002, 43, 4602–4627.
doi:10.1063/1.1504885

  5. Akhiezer, N. and Glazman, I. Theory of Linear Operators in Hilbert Space. Pitman, Boston, 1981.

  6. Posilicano, A. Self-adjoint extensions of restrictions. OaM, 2008, 2, 483–506.

  7. Albeverio, S., Gesztesy, F., Högh-Krohn, R., and Holden, H. Solvable Models in Quantum Mechanics, 2nd ed. AMS, Chelsea, 2005.

  8. Posilicano, P. A Krein-like formula for singular perturbations of self-adjoint operators and applications. J. Funct. Anal., 2001, 183, 109–147.
doi:10.1006/jfan.2000.3730

  9. Berezin, F. and Fadeev, L. Remark on the Schrödinger equation with singular potential. Dokl. Akad. Nauk. SSSR, 1961, 137, 1011–1014.

10. Blanchard, Ph., Figari, R., and Mantile, A. Point interaction Hamiltonians in bounded domains. J. Math. Phys., 2007, 48, 082108.
doi:10.1063/1.2770672

11. Posilicano, A. The Schrödinger equation with a moving point interaction in three dimensions. Proc. Amer. Math. Soc., 2007, 135, 1785–1793.
doi:10.1090/S0002-9939-06-08814-9

12. Kanwal, R. P. Generalized Functions: Theory and Technique, 2nd ed. Birkhäuser, Boston, 1998.

13. Dias, N. C., Posilicano, A., and Prata, J. N. Self-adjoint, globally defined Hamiltonian operators for systems with boundaries. Physics Archives: arXiv:0707.0948, 2007.

14. Voronov, B., Gitman, D., and Tyutin, I. Self-adjoint differential operators associated with self-adjoint differential expressions. Physics Archives: arXiv:quant-ph/0603187, 2006.
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