Quantum mechanical manifestation of order-chaos-order-chaos-type of switch-over in hydrogen molecule ion perturbed with varying magnetic field

Abstract

We manifest, quantum mechanically, the order-chaos-order-chaos-type of switch-over which we observed in our previous work, the classical treatment of hydrogen molecule ion placed in varying magnetic field. We compute the excited state eigenvalues and obtain the corresponding eigenfunctions for the same parameters used in our classical analogue by numerically solving the Schrödinger equation using the python library scipy. With the aid of level statistics with nearest-neighbour spacing distribution and symmetry of the eigenfunctions we ascertain the chaos-order-chaos transit as we increase the strength of the magnetic field in the quantum mechanical perspective.