Abstract
The analytic expression of the time evolution wavefunction of the two-dimensional harmonic oscillator with time-dependent mass and frequency in a static magnetic field is obtained using an operator-algebraic method slightly different from the usual Lie algebraic technique. The evolution operator of the one-dimensional harmonic oscillator with time-dependent mass and frequency is established first by forming an operator differential equation with the su(1, 1) Lie algebra, which is deduced from the time-dependent linear unitary transformation for boson operators (a, a†), and then by comparing this operator equation with the time evolution equation of the one-dimensional oscillator.
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