Construction of exact Ermakov-Pinney solutions and time-dependent quantum oscillators
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- 作者：Sang Pyo Kim ; Won Kim
- 关键词：Time ; dependent oscillator ; Ermakov ; Pinney solution ; Quantum invariant ; Pöschl ; Teller potential
- 刊名：Journal of the Korean Physical Society
- 出版年：2016
- 出版时间：November 2016
- 年：2016
- 卷：69
- 期：10
- 页码：1513-1517
- 全文大小：
- 刊物主题：Physics, general; Theoretical, Mathematical and Computational Physics; Particle and Nuclear Physics;
- 出版者：The Korean Physical Society
- ISSN：1976-8524
- 卷排序：69
文摘
The harmonic oscillator with a time-dependent frequency has a family of linear quantum invariants for the time-dependent Schrödinger equation, which are determined by any two independent solutions to the classical equation of motion. Ermakov and Pinney have shown that a general solution to the time-dependent oscillator with an inverse cubic term can be expressed in terms of two independent solutions to the time-dependent oscillator. We explore the connection between linear quantum invariants and the Ermakov-Pinney solution for the time-dependent harmonic oscillator. We advance a novel method to construct Ermakov-Pinney solutions to a class of time-dependent oscillators and the wave functions for the time-dependent Schrödinger equation. We further show that the first and the second Pöschl-Teller potentials belong to a special class of exact time-dependent oscillators. A perturbation method is proposed for any slowly-varying time-dependent frequency.