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Let  H  be a self‐adjoint isotropic elliptic pseudodifferential operator of order 2. Denote by    u  (  t  )    the solution of the Schrödinger equation    (  i   ∂  t   −  H  )  u  =  0    with initial data    u   (  0  )   =   u  0    . If  u  0  is compactly supported the solution    u  (  t  )    is smooth for small    t  >  0   , but not for all  t . We determine the wavefront set of    u  (  t  )    in terms of the wavefront set of  u  0  and the principal and subprincipal symbol of  H .

Recurrence of singularities for second order isotropic pseudodifferential operators