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Consider the Hamiltonian    H  :  =   h  2   Δ  +  V  –  E    where   Δ   is the positive Laplacian on    R  d   ,    V  ∈   C  0  ∞    (   R  d   )is a smooth, compactly supported potential,    E  >  0    is an energy level, and    h  >  0    is a semiclassical parameter. We study the eigenvalues of the scattering matrixS  h    (  E  )    , which lie on the unit circleS  1   ⊂  C    due to the unitarity ofS  h    (  E  )    . Under an appropriate hypothesis on the classical dynamical flow corresponding to   H  , we show that in the limit    h  →  0   , the eigenvalues are asymptotically equidistributed on the unit circle away from the point    1  ∈   S  1    .

Equidistribution of phase shifts in semiclassical potential scattering