Abstract
The effect of path curvature on kinetic energy in bound state systems has been investigated by solving the Schrödinger equation for a particle confined to an annular region of uniform width. In the one-dimensional limit of a narrow annulus the angular behavior of the particle can be described by linear motion with an effective potential. This potential is related to the radius of curvature R by Veff=−(h/2/2m)(1/4R2). Thus, for a particle confined to a narrow channel high path curvature produces an effective stabilizing influence. An interpretation of this phenomenon is offered and several examples are examined.
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