73 research outputs found
Class of invariants for the 2D time-dependent Landau problem and harmonic oscillator in a magnetic field
We consider an isotropic two dimensional harmonic oscillator with arbitrarily
time-dependent mass and frequency in an arbitrarily
time-dependent magnetic field . We determine two commuting invariant
observables (in the sense of Lewis and Riesenfeld) in terms of some
solution of an auxiliary ordinary differential equation and an orthonormal
basis of the Hilbert space consisting of joint eigenvectors of
. We then determine time-dependent phases such that
the are solutions of the
time-dependent Schr\"odinger equation and make up an orthonormal basis of the
Hilbert space. These results apply, in particular to a two dimensional Landau
problem with time-dependent , which is obtained from the above just by
setting . By a mere redefinition of the parameters, these
results can be applied also to the analogous models on the canonical
non-commutative plane.Comment: 13 pages, 3 references adde
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