标题： 具有线性和/或二次扰动的量子各向异性振子势的有理扩展 显示英文标题

标题： Rational Extension of Quantum Anisotropic Oscillator Potentials with Linear and/or Quadratic Perturbations

摘要： 我们对量子各向异性谐振子(QAHO)势在具有线性和/或二次扰动情况下的有理延拓进行了全面研究。 对于一维谐振子加上虚数线性扰动($i\lambda x$)，我们表明，不仅偶数余维（$m$）的有理延拓是可能的，奇数余维的有理延拓也是可行的。 在二维情况下，我们构建了当$\lambda$为实数或虚数时，具有二次（$\lambda \, xy$）扰动的QAHO势的有理延拓，并得到了它们的解。 最后，我们将讨论扩展到具有线性和二次扰动的三维QAHO势，并得到了相应的有理延拓势。 对于所有这些情况，我们获得了能谱保持实数以及系统存在简并的条件。 显示英文摘要

摘要： We present a comprehensive study of the rational extension of the quantum anisotropic harmonic oscillator (QAHO) potentials with linear and/or quadratic perturbations. For the one-dimensional harmonic oscillator plus imaginary linear perturbation ($i\lambda x$), we show that the rational extension is possible not only for the even but also for the odd co-dimensions $m$. In two-dimensional case, we construct the rational extensions for QAHO potentials with quadratic ($\lambda \, xy$) perturbation both when $\lambda$ is real or imaginary and obtain their solutions. Finally, we extend the discussion to the three-dimensional QAHO with linear and quadratic perturbations and obtain the corresponding rationally extended potentials. For all these cases, we obtain the conditions under which the spectrum remains real and also when there is degeneracy in the system.