Open AccessAdaptive perturbation method in quantum mechanics
Author(s) -
ChenTe Ma
Publication year - 2021
Publication title -
iop scinotes
Language(s) - English
Resource type - Journals
ISSN - 2633-1357
DOI - 10.1088/2633-1357/ac12ba
Subject(s) - perturbation (astronomy) , hamiltonian (control theory) , poincaré–lindstedt method , transition of state , physics , quantum , mathematics , classical mechanics , statistical physics , mathematical analysis , quantum mechanics , mathematical optimization , quantum dynamics
The adaptive perturbation chooses a non-standard decomposition. The Hamiltonian becomes a sum of solvable and perturbation parts. We calculate the spectrum using the adaptive perturbation method at the leading-order to compare to numerical solutions. The maximum deviation is around 5% for different coupling regions. A perturbation study relies on whether a choice of leading-order is suitable. Our result with different parameters should show that the adaptive perturbation method provides appropriate saddle points to all coupling regions. In the end, we show that the perturbation parameters should not be a coupling constant.