@article{oai:oist.repo.nii.ac.jp:00002265,
 author = {Anh-Tai, Tran Duong and Hoang, Duc T. and Truong, Thu D. H. and Nguyen, Chinh Dung and Uyen, Le Ngoc and Dung, Do Hung and Vy, Nguyen Duy and Pham, Vinh N. T.},
 issue = {085310},
 journal = {AIP Advances},
 month = {Aug},
 note = {In this work, we present a rigorous mathematical scheme for the derivation of the sth-order perturbative corrections to the solution to a one-dimensional harmonic oscillator perturbed by the potential V-per(x) = lambda x(alpha), where alpha is a positive integer, using the non-degenerate time-independent perturbation theory. To do so, we derive a generalized formula for the integral I = integral(+infinity)(-infinity)x(alpha)exp(-x(2))H-n(x)H-m(x)d(x), where H-n(x) denotes the Hermite polynomial of degree n, using the generating function of orthogonal polynomials. Finally, the analytical results with alpha = 3 and alpha = 4 are discussed in detail and compared with the numerical calculations obtained by the Lagrange-mesh method.},
 title = {Analytical study of the sth-order perturbative corrections to the solution to a one-dimensional harmonic oscillator perturbed by a spatially power-law potential Vper(x) = λxα},
 volume = {11},
 year = {2021}
}