Chapter 9 The Two-Body Problem



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2. Bibliography
[1] H. Goldstein, C. Poole and J. Safco, Classical Mechanics, Third Edition (Addison-Wesley, San Francisco, 2002).
[2] H.S. Green, Matrix Mechanics, (P. Noordhoff, Netherlands, 1965).
[3] R. L. Liboff, I. Nebenzahl and H.H. Fleischmann, On the radial momentum operator, Am. J. Phys. 41, 976, (1973).
[4] B. Friedman, Principles and Techniques of Applied Mathematics, (John Wiley & Sons, New York, 1957), p. 154.
[5] A.Z. Capri, Nonrelativistic Quantum Mechanics, Third Edition, (World Scientific, 2002), p. 209.
[6] G. Paz, The non-self-adjointness of the radial operator in dimensions, J. Phys. A 35, 3727 (2002).
[7] L.D. Landau and E.M. Lifshitz, Quantum Mechanics, Non-relativistic Theory, (Pergamon Press, London, 1958).
[8] G. Baym, Lectures on Quantum Mechanics, (W.A. Benjamin, Reading,
[9] J. Schwinger in L.C. Biedenharn and H. van Dam, Quantum Theory of Angular Momentum, (Academic Press, New York, 1965), p. 229.
[10] J.J. Sakurai, Modern Quantum Mechanics, (Addison-Wesley, Reading, , p. 217.
[11] M. Born, W. Heisenberg and P. Jordan, Zur Quantenmechanic II, Z. Phys. 35, 557 (1926), translated in B.L. van der Waerden, Sources of Quantum Mechanics, (Dover Publications, New York, 1967), p. 321.
[12] L. Infeld and T.E. Hull, The factorization method, Rev. Mod. Phys. 23, 21
[13] Y.F. Liu, Y.A. Lei and J.Y. Zeng, Factorization of the radial Schrödinger equation and four kinds of the raising and lowering operators of hydrogen atoms and isotropic harmonic oscillators, Phys. Lett. A 231, 9 (1997)
[14] B-W. Xu and F-M. Kong, Factorization of the radial Schrödinger equation of the hydrogen atom, Phys. Lett. A 259, 212 (1999).
[15] J.D. Hey, On the determination of radial matrix elements for high- transitions in hydrogenic atoms and ions, J. Phys. B, 39, 2641 (2006).
[16] W. Pauli, Uber das Wasserstoffspektrum vom Standpunkt der neuen Quantenmechanik, Z. Phys. 36, 336 (1926), translated in Sources of Quantum Mechanics, edited by B.L. van der Waarden, (North-Holland, Amsterdam, 1967), p. 387 ff. [17] M. Taketani and M. Nagasaki, The Formation and Logic of Quantum Mechanics, Vol. III (World Scientific, 2001), p. 336.
[18] H. Goldstein, C. Poole and J. Safco, Classical Mechanics, Third Edition (Addison-Wesley, San Francisco, 2002).
[19] For obtaining the eigenvalues from the wave equation see X.L. Yang, S.H. Guo, F.T. Chan, K.W. Wong and W.Y. Ching, Analytic solution of a twodimensional hydrogen atom. I. Nonrelativistic theory, Phys. Rev. A 43, .
[20] M. Nauenberg, Quantum wave packet on Kepler orbits, Phys. Rev. A 40, .
[21] A wave packet solution for the hydrogen atom for large principal quantum number can be found in L.S. Brown, Classical limit of the hydrogen atom, Am. J. Phys. 41, 525 (1973).
[22] A. Joseph, Self-Adjoint Ladder Operators (I), Rev. Mod. Phys. 39, 829 (1967).
[23] C.A. Coulson and A. Joseph, Self-Adjoint Ladder Operators (II), Rev. Mod. Phys. 39, .
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