Abstract
We study a nonrelativistic charged quantum particle moving in a bounded open set Ω⊂R3 with smooth boundary under the action of a zero-range potential. In the electrostatic case the standing wave solution takes the form ψ(t,x)=u(x)e−iωt where u formally satisfies −Δu+αϕu−1βδx0u=ωu and the electric potential ϕ is given by −Δϕ=u2. We give a rigorous definition of this problem and show that it has a weak nontrivial solution.
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