WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 23, 2024
The Classical Harmonic Oscillator on ℝ Perturbed by a Certain Scalar Potential
Authors: , ,
Abstract: We investigate the perturbation A = H + V, where $$H = \frac{1}{2} \left ( - \frac{d^{2}}{dx^{2}} \right )$$ represents the harmonic
oscillator in \mathbb{R}, and V is a specific scalar potential. Let $$λ_{k}$$ denote the $$k^{th}$$ eigenvalue of the operator H. The
eigenvalues of the perturbed operator L are given by $$λ_{k} + μ_{k}$$ where $$μ_{k}$$ accounts for the perturbative effects of
the potential V . The primary result of this study is to provide an asymptotic expansion of $$μ_{k}$$ and to establish a
connection between the coefficients of this expansion and a particular transform of the potential V .