A constant of quantum motion in two dimensions in crossed magnetic and electric fields

Details A constant of quantum motion in two dimensions in crossed magnetic and electric fields A constant of quantum motion in two dimensions in crossed magnetic and electric fields

2010-06-02

arxiv.org/abs/1006.0326v2

Physics

Mathematical Physics

18 pages, 2 figures; the title was changed and several typos corrected; to appear in J. Phys. A: Math. Theor. 43 (2010)

Scientific paper

We consider the quantum dynamics of a single particle in the plane under the influence of a constant perpendicular magnetic and a crossed electric potential field. For a class of smooth and small potentials we construct a non-trivial invariant of motion. Do to so we proof that the Hamiltonian is unitarily equivalent to an effective Hamiltonian which commutes with the observable of kinetic energy.

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