Список литературыYuri Krynytskyi, Andrij Rovenchak“Asymptotic Estimation for Eigenvalues in the Exponential Potential and for Zeros of $K_{{\rm i}\nu}(z)$ with Respect to Order”, SIGMA, 2021, том 17,057, 7 стр.

Asymptotic Estimation for Eigenvalues in the Exponential Potential and for Zeros of $K_{{\rm i}\nu}(z)$ with Respect to Order
Yuri Krynytskyi, Andrij Rovenchak



Список литературы

1.	Abramowitz M., Stegun I. A. (eds.), Handbook of mathematical functions, with formulas, graphs, and mathematical tables, Dover Publications, Inc., New York, 1966
2.	Ahmed Z., Ghosh D., Kumar S., Turumella N., “Solvable models of an open well and a bottomless barrier: one-dimensional exponential potentials”, Eur. J. Phys., 39 (2018), 025404, 10 pp., arXiv: 1706.05275
3.	Amore P., Fernández M. F., “Accurate calculation of the complex eigenvalues of the Schrödinger equation with an exponential potential”, Phys. Lett. A, 372 (2008), 3149–3152, arXiv: 0712.3375
4.	Bagirova S. M., Khanmamedov A. K., “On zeros of the modified Bessel function of the second kind”, Comput. Math. Math. Phys., 60 (2020), 817–820
5.	Balogh C. B., “Asymptotic expansions of the modified Bessel function of the third kind of imaginary order”, SIAM J. Appl. Math., 15 (1967), 1315–1323
6.	Bethe H. A., Bacher R. F., “Nuclear physics A Stationary states of nuclei”, Rev. Mod. Phys., 8 (1936), 82–229
7.	Bhaduri R. K., Sprung D. W.L., Suzuki A., When is the lowest order WKB quantization exact?, Can. J. Phys., 84 (2006), 573–581, arXiv: gr-qc/0508107
8.	Campbell J., “Determination of $\nu$-zeros of Hankel functions”, Comput. Phys. Comm., 32 (1984), 333–339
9.	Cochran J. A., “The zeros of Hankel functions as functions of their order”, Numer. Math., 7 (1965), 238–250
10.	Cochran J. A., Hoffspiegel J. N., “Numerical techniques for finding $\nu $-zeros of Hankel functions”, Math. Comp., 24 (1970), 413–422
11.	Corless R. M., Gonnet G. H., Hare D. E.G., Jeffrey D. J., Knuth D. E., “On the Lambert $W$ function”, Adv. Comput. Math., 5 (1996), 329–359
12.	Curtis L. J., Ellis D. G., “Use of the Einstein–Brilloui–Keller action quantization”, Amer. J. Phys., 72 (2004), 1521–1523
13.	Dunster T. M., “Bessel functions of purely imaginary order, with an application to second-order linear differential equations having a large parameter”, SIAM J. Math. Anal., 21 (1990), 995–1018
14.	Ferreira E. M., Sesma J., “Zeros of the Macdonald function of complex order”, J. Comput. Appl. Math., 211 (2008), 223–231, arXiv: math.CA/0607471
15.	Guo K.-X., Xiao B., Zhou Y., Zhang Z., “Polaron effects on the third-harmonic generation in asymmetrical semi-exponential quantum wells”, J. Optics, 17 (2015), 035505, 6 pp.
16.	Guo Z.-K., Zhang Y.-Z., “Interacting phantom energy”, Phys. Rev. D, 71 (2005), 023501, 5 pp., arXiv: 1910.06796
17.	Johansson F., “Computing the Lambert $W$ function in arbitrary-precision complex interval arithmetic”, Numer. Algorithms, 83 (2020), 221–242, arXiv: 1705.03266
18.	Kamali V., Motaharfar M., Ramos R. O., “Warm brane inflation with an exponential potential: a consistent realization away from the swampland”, Phys. Rev. D, 101 (2020), 023535, 13 pp., arXiv: 1910.06796
19.	Ma S.T., “Redundant zeros in the discrete energy spectra in Heisenberg's theory of characteristic matrix”, Phys. Rev., 69 (1946), 668–668
20.	Magnus W., Kotin L., “The zeros of the Hankel function as a function of its order”, Numer. Math., 2 (1960), 228–244
21.	Migdal A. B., Krainov V., Approximation methods in quantum mechanics, W.A. Benjamin, Inc., New York – Amsterdam, 1969
22.	Pisanty E., Answer to: Eigenvalues and eigenfunctions of the exponential potential $V(x)=\exp(\|x\|)$, https://physics.stackexchange.com/questions/47128/eigenvalues-and-eigenfunctions-of-the-exponential-potential-vx-expx, 2016
23.	Sasaki R., Znojil M., “One-dimensional Schrödinger equation with non-analytic potential $V(x)=-g^2\exp (-\|x\|)$ and its exact Bessel-function solvability”, J. Phys. A: Math. Theor., 49 (2016), 445303, 12 pp., arXiv: 1605.07310
24.	Sun Y., Xiao J.-L., “Coherence effects of the strongly-coupled optical polaron-level qubit in a quantum well with asymmetrical semi-exponential potential”, Superlattices Microstruct., 145 (2020), 106617, 7 pp.
25.	Vakarchuk I., Quantum mechanics, Lviv University Press, Lviv, 2012
26.	Yesilgul U., Ungan F., Sakiroglu S., Sari H., Kasapoglu E., Sökmen I., “Nonlinear optical properties of a semi-exponential quantum wells: effect of high-frequency intense laser field”, Optik, 185 (2019), 311–316