  The adiabatic theorem is an important concept in quantum mechanics, it tells
that a quantum system subjected to gradually changing external conditions
remains to the same instantaneous eigenstate of its Hamiltonian as it initially
in. In this paper, we study the another extreme circumstance where the external
conditions vary rapidly such that the quantum system can not follow the change
and remains in its initial state (or wavefunction). We call this type of
evolution anit-adiabatic evolution. We examine the matter-wave pressure in this
situation and derive the condition for such an evolution. The study is
conducted by considering a quantum particle in an infinitely deep potential,
the potential width $Q$ is assumed to be change rapidly. We show that the total
energy of the quantum subsystem decreases as $Q$ increases, and this rapidly
change exerts a force on the wall which plays the role of boundary of the
potential. For $Q<Q_{0}$ ($Q_0$ is the initial width of the potential), the
force is repulsive, and for $Q>Q_{0}$, the force is positive. The condition for
the anti-adiabatic evolution is given via a spin-$\frac 1 2$ in a rotating
magnetic field.
