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Bound States and the Interaction Representation
Phys. Rev. 87, 652 – Published 15 August, 1952
DOI: https://doi.org/10.1103/PhysRev.87.652
Abstract
The temporal development of the state vectors in the interaction representation is investigated for a quantum-mechanical system that has bound states. It is shown that there is a non-unitary operator which determines the variation of the state vectors of the free states. This operator satisfies the same differential equation and initial condition as the unitary operator which transforms a state vector at the remote past to the state vector at a finite time or in the remote future. The present investigation is relevant to a remark made by H. S. Snyder.
No iteration process is made use of in the general investigation. Born's method of successive approximations is discussed at the end.
References (15)
- W. Heisenberg, Z. Physik 1, 608 (1946) C. Møller, Kgl. Danske Videnskab. Selskab, Mat.-fys. Medd. 23, No. 1 (1945) ibid.22, No. 19 (1946) W. Pauli, Meson Theory of Nuclear Forces (Interscience Publishers, New York, 1948) G. Wentzel, Revs. Modern Phys. 19, 1 (1947)
- W. Heitler, Quantum Theory of Radiation (Oxford University Press, London, 1944) E. C. G. Stueckelberg, Helv. Phys. Acta 18, 195 (1945) S. Tomonaga, Prog. Theoret. Phys. 1, 27 (1946) J. Schwinger, Phys. Rev. 74, 1439 (1948) R. P. Feynman, 76, 749, 769 (1949) F. J. Dyson, 75, 486, 1736 (1949) D. Rivier, Helv. Phys. Acta 22, 265 (1949) K. O. Friedrichs, Commun. Pure Appl. Math. 5, 1 (1952)
- K. O. Friedrichs, Commun. Pure Appl. Math. 1, 361 (1948) B. A. Lippmann and J. Schwinger, Phys. Rev. 79, 469 (1950) H. S. Snyder, 83, 1154 (1951) M. Schoenberg, Nuovo cimento 8, 403, 651 (1951) E. Arnous and S. Zienau, Helv. Phys. Acta 24, 279 (1951) J. Pirenne, Phys. Rev. 86, 395 (1952)
- W. Heitler and S. T. Ma, Proc. Irish Academy 52 A, No. 9, 109 (1949) E. Arnous and S. Zienau ([3]) M. Schoenberg, Nuovo cimento 8, 817 (1951)
- Y. Nambu, Prog. Theoret. Phys. 5, 82 (1950) E. E. Salpeter and H. A. Bethe, Phys. Rev. 84, 1232 (1951) J. Schwinger, Proc. Natl. Acad. Sci. 37, 452, 455 (1951) M. Gell-Mann and F. Low, Phys. Rev. 84, 350 (1951) M. Jean, Compt. rend. 233, 602 (1951)
- B. Ferretti, Nuovo cimento 8, 108 (1951) F. J. Dyson, Phys. Rev. 82, 428 (1951) ibid.83, 608, 1207 (1951) K. Nishijima, Prog. Theoret. Phys. 6, 37 (1951)
- P. A. M. Dirac, Principles of Quantum Mechanics (Oxford University Press, London, 1947)
- P. A. M. Dirac, Principles of Quantum Mechanics (Oxford University Press, London, 1947)
Omitted endnote
- L. Hulthén, Kgl. Fysiograf. Sällskap. Lund. Förh. 14, No. 21 (1944) B. A. Lippmann and J. Schwinger ([3]) M. L. Goldberger, Phys. Rev. 84, 929 (1951)
- M. Schoenberg ([3]) M. Gell-Mann and F. Low ([5]) G. F. Chew and G. C. Wick, Phys. Rev. 85, 636 (1952) J. Ashkin and G. C. Wick, 85, 686 (1952)
- M. Neuman Phys. Rev. 83, 671 (1951)
Omitted endnote
- R. Jost and A. Pais, Phys. Rev. 82, 840 (1951) F. J. Dyson, 85, 631 (1952)
Omitted endnote