Dobrokhotov, S. Yu.; Kolokoltsov, V. N.; Maslov, V. P. Quantization of the Bellman equation, exponential asymptotics and tunneling. (English) Zbl 0796.35141 Maslov, V. P. (ed.) et al., Idempotent analysis. Transl. ed. by A.B. Sossinskij. Providence, RI: American Mathematical Society. Adv. Sov. Math. 13, 1-46 (1992). Our paper is devoted to the derivation of the asymptotics of the low eigenfunctions of the Schrödinger operator obtained by investigating large time asymptotics for the equation \[ h {\partial u \over \partial t} = \left( {h^ 2 \over 2} \Delta-v(x) \right) u. \]For the entire collection see [Zbl 0772.00015]. Cited in 4 Documents MSC: 35Q40 PDEs in connection with quantum mechanics 35B40 Asymptotic behavior of solutions to PDEs 35F20 Nonlinear first-order PDEs 90C27 Combinatorial optimization 81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory Keywords:asymptotics of the low eigenfunctions of the Schrödinger operator; large time asymptotics PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Adv. Sov. Math. 13, 1--46 (1992; Zbl 0796.35141)