Abstract
A boundary condition at t = ± ∞ (t being the “relative” time variable) is obtained for the four-dimensional wave function of a two-body system in a bound state. It is shown that this condition implies that the wave function can be continued analytically to complex values of the “relative time” variable; similarly the wave function in momentum space can be continued analytically to complex values of the “relative energy” variable P 0. In particular one is allowed to consider the wave function for purely imaginary values of t, or respectively p 0, i.e., for real values of x 4 = ict and p 4 = ip 0. A wave equation satisfied by this function is obtained by rotation of the integration path in the complex plane of the variable p 0, and it is further shown that the formulation of the eigenvalue problem in terms of this equation presents several advantages in that many of the ordinary mathematical methods become available.
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References
E. E. Salpeter and H. A. Bethe, Phys. Rev. 84, 1232 (1951);
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M. Gell-Mann and F. Low, Phys. Rev. 84, 350 (1951).
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© 1988 Kluwer Academic Publishers
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Wick, G.C. (1988). Properties of Bethe-Salpeter Wave Functions. In: Noz, M.E., Kim, Y.S. (eds) Special Relativity and Quantum Theory. Fundamental Theories of Physics, vol 33. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3051-3_18
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DOI: https://doi.org/10.1007/978-94-009-3051-3_18
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7872-6
Online ISBN: 978-94-009-3051-3
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