We investigate the spectral and eigenstate properties of the quantum superexponential oscillator. Our focus is on the quantum signatures of the recently observed transition of the energy dependent period of the corresponding classical superexponential oscillator. We show that the ground state exhibits a remarkable metamorphosis of decentering, asymmetrical squeezing and the development of a tail. Analyzing the central moments up to high order a characteristic transition from exponentially decaying moments to increasing moments is unravelled. A corresponding spectral analysis shows that, surprisingly, to a good approximation the spectrum is equidistant. A closer look, however, reveals a spectral scaling behaviour below the transition point which is replaced by irregular oscillations above the transition energy. Excited bound states are analyzed up to the continuum threshold. We discuss future perspectives and possible experimental realizations of the superexponential oscillator.<...

中文翻译：

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量子超指数振荡器

我们研究了量子超指数振荡器的光谱和本征态特性。我们的重点是相应经典超指数振荡器的能量相关周期最近观察到的跃迁的量子特征。我们表明，基态表现出明显的变心，偏心，不对称挤压和尾巴的发展。分析中心矩直至高阶的过程，从指数衰减矩到增加矩的特征过渡都没有被阐明。相应的光谱分析表明，令人惊讶的是，光谱近似等距。然而，仔细观察，发现过渡点以下的光谱缩放行为被过渡能量以上的不规则振荡所取代。分析激发的束缚态直至连续阈值。我们讨论超指数振荡器的未来前景和可能的实验实现。