| A Quantum Pipette (2007) | |||||||||||||||
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| Introduction Though numerous quantum phenomena can be explained by usual semiclassical concepts, a complete theory --- even in the case of the nonrelativistic quantum mechanics --- is certainly deeper. A recent illustration was provided by properties of particles within bent tubes or other infinitely extended regions with Dirichlet boundaries (i.e., hard walls). It was demonstrated that such systems exhibit isolated energy eigenvalues [7, 8, 11] despite the absence of closed trajectories (apart of the obvious zero--measure set) in their classical counterparts. These bound states and related resonance effects in scattering [4] have attracted a considerable interest --- a list of references can be found in the review paper [3]. It is motivated not only by the mentioned theoretical reason, but rather by the fact that curved tubes (and more complicated regions constructed of them) can model some real physical systems. The most prominent among them are quant | |||||||||||||||
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