Prog. Theor. Phys. Vol. 77 No. 5 (1987) pp. 1232-1239
Quantization Formula for the Schrödinger Equation with Repulsive Potential
Department of Physics, University of the Ryukyus, Okinawa 903-01
*Department of Matehmatics, University of the Ryukyus, Okinawa 903-01
(Received October 25, 1986)
We consider the Schrödinger equation with potential V(r) which decreases rapidly to -∞ as r→∞. Although the classical motion is unbounded in this case, there are quantum bound states nvertheless. An exact formula which gives the distribution of the eigenvalues is presented. To obtain this formula, the method developed by Milne, Ezawa, Larsen and others is used.
DOI : 10.1143/PTP.77.1232
- J. von Neumann and E. P. Wigner, Phys. Z. 30 (1929), 465.
F. H. Stillinger and D. R. Herrick, Phys. Rev. A11 (1975), 446[APS].
J. M. F. Gunn, Eur. J. Phys. 7 (1986), 29[IoP STACKS].
S. Matsumoto, K. Kakazu and T. Nagamine, J. Math. Phys. 27 (1986), 232[CrossRef].
W. E. Milne, Phys. Rev. 35 (1930), 863[APS].
- H. Ezawa, K. Nakamura and Y. Yamamoto, Proc. Japan Acad. 46 (1970), 168.
- U. Larsen, J. of Phys. A16 (1983), 2137; Phys. Lett. 105A (1984), 179.
- M. H. Stone, Am. Math. Soc., Providence, RI, XV (1932).