Abstract
We obtain the exact solutions of a single particle magneto-confined in a one-dimensional (1D) quantum wire with a single square barrier. Theoretical analysis and numerical computation show that for a set of fixed barrier height and width, the quantum levels and states of the system depend on the displacement d of the magnetic trap, and for a fixed d value the system occupies only one or two lower quantum levels of n ≤ 20 of a free harmonic oscillator. In the barrier region, the finite-sized effect implies that only for some discrete barrier parameters and d values, the system has the Hermitian polynomial solutions, otherwise it has the infinite series solutions. Therefore, one can manipulate the external motional states of the system and prepare some required lower energy states by adjusting the displacement of the magnetic trap experimentally.
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