一个新的具有可调基态的双参数势族
A New Two-Parameter Family of Potentials with a Tunable Ground State
摘要：
在前一篇文章中，我们通过证明一维薛定谔方程是标准量子谐振子的超对称伙伴势，从而求解了可数无限族的一维薛定谔方程。在这项工作中，我们将这些结果扩展到找到完整的一套真正的合作伙伴的潜力的谐振子，表明这些依赖于两个连续的参数。除了基态能量成为一个可调参数外，它们的光谱与谐振子的光谱相同。最后利用这些势分析了陷在凹坑势中的原子气体中的玻色-爱因斯坦凝聚的物理问题。
英文摘要：
In a previous paper we solved a countably infinite family of one-dimensional Schrödinger equations by showing that they were supersymmetric partner potentials of the standard quantum harmonic oscillator. In this work we extend these results to find the complete set of real partner potentials of the harmonic oscillator, showing that these depend upon two continuous parameters. Their spectra are identical to that of the harmonic oscillator, except that the ground state energy becomes a tunable parameter. We finally use these potentials to analyse the physical problem of Bose-Einstein condensation in an atomic gas trapped in a dimple potential.
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