Abstract
The ground state of a particle confined to two two-dimensional square boxes connectedwith a narrow channel is calculated. It is shown that the presence of the channel results inthe splitting of the otherwise degenerate ground state. When the width of the channel issmall compared to the wavelength of the particle, the wavefunction in the channelis exponentially suppressed, very much like in the case of tunnelling through apotential barrier. Moreover, in the limit of long and narrow channels, any smallasymmetry in the shape of the boxes results in the localization of the particle.
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