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

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