Distributed Phase Acquisition in a Wave Function

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A separable x-y model is solved for a specialized vector potential (no magnetic and weak electric fields) penetrating slowly, adiabatically into and across a rectangular box to which an electron is confined. The time-dependent Schrödinger equation has adiabatic solutions, in which gradual phase acquisitions occur for parts of the electronic wave function. For a closed trajectory of the source, the initial and after-return wave functions are shown to be simultaneously co-degenerate solutions of the Hamiltonian, which situation repeats itself for further cyclic motion of the source.