Abstract We construct a time-dependent double well potential as an exact spectral equivalent to the explicitly time-dependent negative quartic oscillator with a time-dependent mass term. Defining the unstable anharmonic oscillator Hamiltonian on a contour in the lower-half complex plane, the resulting time-dependent non-Hermitian Hamiltonian is first mapped by an exact solution of the time-dependent Dyson equation to a time-dependent Hermitian Hamiltonian defined on the real axis. When unitary transformed, scaled and Fourier transformed we obtain a time-dependent double well potential bounded from below. All transformations are carried out non-perturbatively so that all Hamiltonians in this process are spectrally exactly equivalent in the sense that they have identical instantaneous energy eigenvalue spectra.

中文翻译：

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光谱等效的瞬态双井和不稳定的非谐振荡器

摘要 我们构建了一个与时间相关的双阱势，作为一个精确的光谱等效于具有时间相关质量项的显式时间相关负四次振荡器。在下半复平面的轮廓上定义不稳定的非谐振荡器哈密顿量，所得的时间相关的非厄米哈密顿量首先通过时间相关的戴森方程的精确解映射到时间相关的厄米哈密顿量。实轴。当幺正变换、缩放和傅立叶变换时，我们获得了一个从下方有界的与时间相关的双阱势。所有变换都是非微扰地进行的，因此在这个过程中的所有哈密顿量在谱上完全等效，因为它们具有相同的瞬时能量特征值谱。