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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].

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
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