Programme

P.44 -- Poster, VCTP-46

Date: Wednesday, 6 October 2021

Time: 08:30 - 10:00

The second–order correction of the energy of one – dimensional harmonic oscillator influenced by position-dependent perturbed potentials

Duc T. Hoang (1), Thang N. Tran (1), Tuan L. A. Nguyen (1), Khang M. Le (1), Tran Duong Anh-Tai (2), Vinh N. T. Pham (1).

(1) Department of Physics, Ho Chi Minh City University of Education, Ho Chi Minh, Vietnam (2) Quantum Systems Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904-0495, Japan

In this work, the energy of arbitrary state of one – dimensional harmonic oscillator in the perturbed spatially dependent potentials $V_n(x) = \lambda x^2$ has been analytically derived using the time-independent perturbation theory up to second ordered correction. Here, a straightforward approach using the generating functions is taken into account to solve the integrals of the production of two arbitrary-order Hermite polynomials. The analytical formulae are in good agreement with previous studies and are numerically validated by the Lagrange-mesh method.

Presenter: Pham Nguyen Thanh Vinh