2017/10/02 by Chun-Khiang Chua, Chua, Chun-Khiang, Yu-Tsai Liu +3
Physics and Astronomy · #FOS: Physical sciences #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1710.00509
openalex publication_date 2017/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The one-dimensional time-independent Green's function G0 of a quantum\nsimple harmonic oscillator system (V0(x)=m \ω2 x2/2) can be obtained\nby solving the equation directly. It has a compact expression, which gives\ncorrect eigenvalues and eigenfunctions easily. The Green's function G with an\nadditional delta-function potential can be obtained readily. The same technics\nof solving the Green's function G0 can be used to solve the eigenvalue\nproblem of the simple harmonic oscillator with an generic delta-function\npotential at an arbitrary site, i.e. V1(x)\∝ \δ(x-a). The\nWronskians play an important and interesting role in the above studies.\nFurthermore, the approach can be easily generalized to solve the quantum system\nof a simple harmonic oscillator with two or more generic delta-function\npotentials. We give the solutions of the case with two additional\ndelta-functions for illustration.\n