Constructing quantum observables and self-adjoint extensions of symmetric operators. I

Russian Physics Journal

Volumn 50, Issue 1, 2007, Pages 1-31

  Voronov, B L ^a   Gitman, D M ^b   Tyutin, I V ^a  

^a LEBEDEV PHYSICAL INSTITUTE   (Russian Federation)

^b UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34250157058     PISSN: 10648887     EISSN: 15739228     Source Type: Journal    
DOI: 10.1007/s11182-007-0001-z     Document Type: Article

References (20)

1. J. von Neumann, Mathematische Grundlagen der Quantenmechanik, Verlag von Julius Springer, Berlin (1932).
2. L. D. Faddeev and O. A. Yakubovsky, Lectures on Qunatum Mechanics, Leningrad State University Press, Leningrad (1980).
3. F. A. Berezin and M. A. Shubin, Schrödinger Equation, Kluwer Publ., New York, Amsterdam (1991).
4. F. A. Berezin and L. D. Faddeev, Sov. Math. Dokl., 12, 372-375 (1961).
5. J. von Neumann, Mat. Ann., 1102, 49-131 (1929).
6. M. H. Stone, Linear Transformations in Hilbert Space and Their Applications to Analysis, Amer. Math. Soc., Colloquium Publications, Vol. 15, Amer. Math. Soc., New York (1932).
7. F. Riesz and B. Sz.-Nagy, Lecons d'Analyse Fonctionnel, Akademiai Kiado, Budapest (1972).
8. N. Dunford and J. T. Schwartz, Linear Operators, Part II, Interscience Publishers, New York, London (1963).
9. N. I. Akhiezer and I. M. Glazman, Theory of Linear Operators in Hilbert Space, Pitman, Boston (1981).
10. M. A. Naimark, Theory of Linear Differential Operators [Russian translation], Nauka, Moscow (1969).
11. V. C. L. Hutson and J. S. Pym, Applications of Functiomal Analysis and Operator Theory, Academic Press, London (1980).
12. A. V. Kuzhel and S. A. Kuzhel, Regular Extensions of Hermitian Operators, VSP, Utrecht (1998).
13. K. M. Case, Phys. Rev. 80, 797-806 (1950).
14. N. F. Mott and H. S. W. Massey, Theory of Atomic Collisions, Oxford University Press, Oxford (1933).
15. I. E. Tamm, Phys. Rev. 58, 952 (1940).
16. H. C. Corben and J. Schwinger, Phys. Rev. 58, 953-968 (1940).
17. M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. II, Academic Press, New York (1972).
18. R. D. Richtmyer, Principles of Advanced Mathematical Physics, Vol. 1, Springer-Verlag, New York-Hidelberg-Berlin (1978).
19. D. Shin, Mat. Sborn., 13 (55), 39-70 (1943).
20. W. N. Everitt, Math. Ann. 149, 320-340 (1963).