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Adiabatic excitation of a confined particle in one dimension with a variable infinitely sharp wall

It is shown that adiabatic cycles excite a quantum particle, which is confined in a one-dimensional region and is initially in an eigenstate. During the cycle, an infinitely sharp wall is applied and varied its strength and position. After the completion of the cycle, the state of the particle arrives another eigenstate. It is also shown that we may vary the final adiabatic state by choosing the parameters of the cycle. With a combination of these adiabatic cycles, we can connect an arbitrary pair of eigenstates. Hence, these cycles may be regarded as basis of the adiabatic excitations. A detailed argument is provided for the case that the particle is confined by an infinite square well. This is an example of exotic quantum holonomy in Hamiltonian systems.