  Superoscillations occur when a globally band-limited function locally
oscillates faster than its highest Fourier coefficient. We generalize this
effect to arbitrary quantum mechanical operators as a weak value, where the
preselected state is a superposition of eigenstates of the operator with
eigenvalues bounded to a range, and the postselection state is a local
position. Superbehavior of this operator occurs whenever the operator's weak
value exceeds its eigenvalue bound. We give illustrative examples of this
effect for total angular momentum and energy. In the later case, we demonstrate
a sequence of harmonic oscillator potentials where a finite energy state
converges everywhere on the real line, using only bounded superpositions of
states whose asymptotic energy vanishes - "energy out of nothing". This limit
requires postselecting the particle in a region whose size diverges in the
considered limit. We further show that superenergy behavior implies that the
state superoscillates in time with a rate given by the superenergy divided by
the reduced Planck's constant. This example demonstrates the possibility of
mimicking a high-energy state with coherent superpositions of nearly
zero-energy states for as wide a spatial region as desired. We provide
numerical evidence of these features to further bolster and elucidate our
claims.
