In terms of SU (1, 1) algebra, the eigen equations of three-dimensional HarmonicOscillator and hydrogen atom in inverse square potential are counterchanged the same equations in form.
The external potential has many forms, such as harmonicoscillatorpotential, optical lattice potential, elliptic function potential, double well potential, and so on.
外势有许多形式：简谐外势、光晶格外势、椭圆函数外势、双阱外势以及含时线性外势等等。
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Using the periodic orbit theory, we computed the quantum level density of a particle in the two-dimensional harmonicoscillatorpotential with and without the magnetic flux line for different cases.