关键词: PT 对称, delta 函数势, 傅里叶变换, 非厄米量子力学

Abstract: Systems with PT symmetry are a hot topic in quantum mechanics research. The bound state problem in one-dimensional PT-symmetric delta potential well is the most simplified model of PT system, and its exact solution is a teaching problem with scientific research value. In this work, the effect of PT symmetry on the bound state and the intrinsic energy of a system is studied by solving the stationary Schrdinger equation of one-dimensional PT-symmetric delta potential. Firstly, the stationary Schrdinger equation of one-dimensional PT-symmetric delta potential is solved and discussed by Fourier transform. Secondly, the contours of the bound states and the intrinsic energies of the system are determined by numerical means. Finally, the relationship between PT symmetry potential strength and intrinsic energy is analyzed and discussed. In this paper, the traditional Hermitian delta potential well eigenvalue problem is extended to non-Hermitian delta potential well problem, which is a useful and timely extension of the necessary exercises in quantum mechanics teaching.

Key words: PT symmetry, delta potential well, Fourier transform, non-Hermitian quantum mechanics