| A simplified two-dimensional model of a quantum particle which interacts with another one through a one-dimensional Morse potential is studied. It is examined to what degree a small deformation of this one-dimensional interaction channel influences the ground state energy. The problem is important for the discussion on the deformation of various kinds of nanosurfaces such as carbon nanotubes. A deformation passing from the straight line geometry to ring geometry is considered. An upper bound for the number of oscillatory states is estimated and it is related to the deformation. |
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