Abstract
The Maslov index in the semiclassical Bohr–Sommerfeld quantization rule is calculated for one-dimensional power-law potentials V (x) = −V 0/x s, x > 0, 0 < s < 2 The result for the potential V(x)=-V 0/x 1/2 is compared with the recently reported exact solution. The case of a spherically symmetric power-law potential is also considered.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
V. P. Maslov, Asymptotic Methods and Perturbation Theory (Nauka, Moscow, 1988) [in Russian].
V. P. Maslov and M. V. Fedoriuk, Semiclassical Approximation in Quantum Mechanics (Nauka, Moscow, 1976; Reidel, Dordrecht, 1981).
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 3: Quantum Mechanics: Non-relativistic Theory (Fizmatlit, Moscow, 2004; Pergamon, New York, 1977).
V. M. Galitskii, B. M. Karnakov, and V. I. Kogan, Problems in Quantum Mechanics (Nauka, Moscow, 1992), Probl. 9.5 [in Russian].
A. M. Ishkhanyan, Eur. Phys. Lett. 112, 10006 (2015).
G. Szegö, Orthogonal Polynomials (Am. Math. Soc., New York, 1959; GIFML, Moscow, 1962).
B. M. Karnakov and V. P. Krainov, WKB Approximation in Atomic Physics (Springer, Berlin, 2013).
C. Quigg and J. L. Rosner, Phys. Rep. 56, 167 (1979).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.M. Ishkhanyan, V.P. Krainov, 2017, published in Pis’ma v Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2017, Vol. 105, No. 1, pp. 34–37.
Rights and permissions
About this article
Cite this article
Ishkhanyan, A.M., Krainov, V.P. Maslov index for power-law potentials. Jetp Lett. 105, 43–46 (2017). https://doi.org/10.1134/S0021364017010106
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021364017010106