Abstract
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.
Highlights
The spectrum of black-body radiation does not have a precise match from classical physics
Because the spectrum is only solvable in a few systems, people use a perturbation method to study quantum physics in a weakly interacting system
We study a model from an exact solution of the solvable part
Summary
The spectrum of black-body radiation does not have a precise match from classical physics. Because the spectrum is only solvable in a few systems, people use a perturbation method to study quantum physics in a weakly interacting system. One introduced a variable without changing the canonical relation [6, 7] We determine this variable by the minimized expectation value of the energy with a Fock state [6, 7]. We analyze the deviation of the spectrum between the solvable part and the numerical solution for different parameters. The adaptive perturbation method at the leading-order already shows a quantitative result in the strongly coupled region. For a high quantum number, it becomes harder to obtain an accurate result from a numerical study This result shows that the adaptive perturbation method is quite helpful for such a region. We define the deviation as 100 × (Numerical Solution) − En(γ)min (Numerical Solution) % in all Tables
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