三维各向同性谐振子的超对称伴随势

The Supersymmetric Partner Potentials of Three Dimensional Harmonic Oscillator

分别用基态和激发态生成超对称势的方法,研究了三维各向同性的谐振子的超对称伴随势,求得了一些伴随势,并对其中具有完全相同能级的势场做了比较和分析,发现这两种方法求得的具有完全相同能级的势场是形式不同且具有不同奇点数的可解势。第一种方法产生的伴随势与原势具有形状不变性,而另一种方法产生的伴随势就未必具有形状不变性。

Through generating the superpotentials from the ground state and the excited state, the supersym-metric partner potentials of the three-dimensional harmonic oscillator potential were studied. Some of them were obtained. Then, some comparison and analysis to the potentials which had the same spectrum were made. By capari-soning, we could discover that the two partner potentials, which based on two different ways but had the identical spectrum, had different mathematical forms and different numbers of singularity. In addition, the supersymmetric partner potentials which were produced by the first way and the original potential were always the shape invariant, but the potentials which were produced by another way were not always like this.