量子非谐振子和双势阱模型中的六次与八次混合非谐项的基态能隙

The Ground-State Energy Gap of Sexic-Octic Mixed Anharmonicities in the Quantum Anharmonic Oscillator and the Double-Well Potential

量子非谐振子和双势阱是重要的数学物理模型,其中,计算源自于非简谐项的基态能隙是一个重要的问题。对于含有纯非谐项的情况,我们最近的研究发现可以用同一个公式来描述它们源自于纯非谐项的基态能隙,意味着这两个模型中的非谐效应存在着某种联系。上述发现是关于的纯非谐项的情况,在本文中我们将继续关注含有混合非谐项的情况,我们计算了六次与八次混合非谐项所产生的基态能隙,发现它们仍然由同样的公式来描述,从而进一步确认了这种未知联系的存在性。

The quantum anharmonic oscillator and the double-well potential models are important mathe-matical physics models in which the ground-state energy gap coming from the anharmonic terms is an important topic. For the case of pure anharmonic term, we find a qualitative formula that de-scribes the ground-state energy gap of both the anharmonic oscillator and the double-well poten-tial, which means that there is some connection between the anharmonic effects in the two models. The above discovery is about the case of pure anharmonic term, in this paper we will continue to focus on the case with mixed anharmonic term, we study this energy gap for the case of the sex-tic-octic mixed anharmonic term, and find that they are still described by the same qualitative formula, thus further confirming the existence of this unknown connection.