  Motivated by $T\bar T$, we introduce and study a wide class of solvable
deformations of quantum-mechanical theories. These deformations map the
Hamiltonian to a function of itself. We solve these theories by computing all
finite-temperature correlation functions of the deformed theory in terms of the
correlators of the undeformed theory. Applications to AdS/CFT, SYK, and the
Schwarzian theory are considered. We write down the deformed Schwarzian action
for an arbitrary Hamiltonian deformation and find that the maximal Lyapunov
exponent is unchanged.
