Quantum properties of two-dimensional linear harmonic oscillator in polar coordinate system
Kaiqiang Xie, Xingrong Zheng, Jingtong Chen, Yujie Li · Journal of Physics Conference Series · 2021
Abstract Using quantum theory and MATLAB software, the basic properties of two-dimensional linear harmonic oscillators in quantum mechanics are systematically studied in polar coordinate system, and obtain the visualized results. The results show that, in polar coordinate system, with the exception of special case nr =0, |m|=0, the degeneracy of two-dimensional linear harmonic oscillator is 2nr +|m|+1, and the corresponding energy eigenvalues is ħω (2nr +|m|+1). The number of intersection line between wave function and the plane with ψ=0 is 2nr +m. In the case of nr =0, the maximum number of probability density distributions is 2|m|. The results of this visualization are in complete agreement with the theoretical results. The visualization results in different coordinate systems can be verified with each other, which opens up a new research idea and also provides an idea for other quantum theoretical models to be studied.