Bound States Energies of a Harmonic Oscillator Perturbed by Point Interactions

• 来源期刊: 理论物理通讯（英文版）
• 年，卷（期）: 2017,（3）
• 页码范围: 241-249
• 页数: 9页
• 语种: 英文
• DOI: 10.1088/0253-6102/67/3/241

摘要

We determine explicitly the exact transcendental bound states energies equation for a one-dimensional harmonic oscillator perturbed by a single and a double point interactions via Green's function techniques using both momentum and position space representations.The even and odd solutions of the problem are discussed.The corresponding limiting cases are recovered.For the harmonic oscillator with a point interaction in more than one dimension,divergent series appear.We use to remove this divergence an exponential regulator and we obtain a transcendental equation for the energy bound states.The results obtained here are consistent with other investigations using different methods.