论文标题
非平稳变形奇异振荡器：量子不变和分解方法
Nonstationary deformed singular oscillator: quantum invariants and the factorization method
论文作者
论文摘要
引入了与固定奇异振荡器相关的时间依赖电位的新家族。这是在注意到可以为单数振荡器构建非固定量子不变性后实现的。这样的不变取决于与Ermakov方程溶液相关的系数，后者变得至关重要，因为它可以保证每次解决方案的规律性。在这种形式中，将分解方法应用于量子不变的而不是哈密顿量后，人们设法将时间参数引入转换中，从而导致分解的操作员，这是新的时间依赖性电位运动的常数。在适当的限制下，初始量子不变剂减少了固定的奇异振荡器哈密顿量，在这种情况下，人们通过常规分解方法收回了获得的潜力家族，并在文献中报道了。此外，讨论了一些特殊的限制，以使潜在的奇异障碍消失，从而导致非单位时间依赖性电位。
New families of time-dependent potentials related with the stationary singular oscillator are introduced. This is achieved after noticing that a non stationary quantum invariant can be constructed for the singular oscillator. Such invariant depends on coefficients that are related to solutions of an Ermakov equation, the latter becomes essential since it guarantees the regularity of the solutions at each time. In this form, after applying the factorization method to the quantum invariant, rather than the Hamiltonian, one manages to introduce the time parameter into the transformation, leading to factorized operators which are the constants of motion of the new time-dependent potentials. Under the appropriate limit, the initial quantum invariant reduces to the stationary singular oscillator Hamiltonian, in such case, one recovers the families of potentials obtained through the conventional factorization method and previously reported in the literature. In addition, some special limits are discussed such that the singular barrier of the potential vanishes, leading to non-singular time-dependent potentials.
