资 源 简 介
Leaky wires in quantum mechanics can be studied as singular perturbations of Hamiltonian with a zero-measure support ( a curve for instance). Such approcah is very fruitful. The mathematical background was created by Alessandro Teta. He used quadratic forms to get resolvents of such Hamiltonians.
Then appeared basic article on this topic:
J.F. Brasche, P. Exner, Yu.A. Kuperin, P. Seba:Schrödinger operators with singular interactions, J. Math. Anal. Appl. 184 (1994), 112-139.
All subsequent works refer to that one.
It is quite difficult to calculate spectrum of a leaky quantum graph directly. But not long ago appeared an article
see (http://arxiv.org/PS_cache/math-ph/pdf/0306/0306033v1.pdf)
where was described the way to approximate a leaky quantum graph by a set of point singular perturbations distributed along a curve.
Using this result we are going to calculate spectrums and find wave functions of complicated leaky quantum graphs which appe
