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The quantum Goos-H\"{a}nchen shift for ballistic electrons is investigated ina parabolic potential well under a uniform vertical magnetic field. It is foundthat the Goos-H\"{a}nchen shift can be negative as well as positive, andbecomes zero at transmission resonances. The beam shift depends not only on theincident energy and incidence angle, but also on the magnetic field and Landauquantum number. Based on these phenomena, we propose an alternative way torealize the spin beam splitter in the proposed spintronic device, which cancompletely separate spin-up and spin-down electron beams by negative andpositive Goos-H\"{a}nchen shifts.

Controllable Goos-H\"{a}nchen shifts and spin beam splitter for ballistic electrons in a parabolic quantum well under a uniform magnetic field