The difference Schrӧdinger equation ψ(z+h)+ψ(z−h)+v(z)ψ(z) = Eψ(z), z ∈ ℂ, is considered, where h > 0 and E ∈ ℂ are parameters and v is a function analytic in a bounded domain D ⊂ ℂ. An asymptotic method is developed for studying its solutions in the domain D for small positive h. Bibliography: 4 titles.
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Dedicated to Vasilii Mikhailovich Babich, brilliant scientist and remarkable person
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 438, 2015, pp. 236–256.
Translated by N. B. Lebedinskaya.
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Fedotov, A.A., Shchetka, E.V. The Complex WKB Method for Difference Equations in Bounded Domains. J Math Sci 224, 157–169 (2017). https://doi.org/10.1007/s10958-017-3402-8