摘要
This work studies Schrodinger equation involving a complex potential. The Hamiltonian is non- Hermitian, non- PT symmetry and non-pseudo-Hermitian. We solve three such kinds of Hamiltonian, including an imaginary potential hump in an infinite well, the imaginary barrier potential by itself, and the imaginary delta potential. All the properties and techniques in quantum mechanics can be bought out to examine if they can be generalized to such a complex potential, for instance, can the standard perturbation theory be applied to a complex perturbation, is there an analogy to the Fano resonance, do the eigenfunctions form a complete basis, or if the path-integral formalism still valid, etc.
並列摘要
HASH(0x1c481010)
並列關鍵字
complex potential ； imaginary potential ； real eigen-energy ； complex eigen-energy ； source ； sink參考文獻
[3] Paul K. Townsend, arXiv:0711.5178v2 [math-ph] 2007
[5] Principles of Quantum Mechanics, by R. Shankar.
[7] H. F. Jones , Phy. Rev. D 76,125003 (2007)
[1] S.A. Yahiaoui, M. Bentaiba, arXiv:0711.2262v1 [math-ph] 14 Nov 2007
[2] Ozlem Yesiltas, Ramazan Sever, arXiv : quant-ph/070155v1 22 Jan 2007
延伸閱讀
- Kee, L. K. (2018). 以保結構算則求解非線性薛丁格方程 [master's thesis, National Taiwan University]. Airiti Library. https://doi.org/10.6342/NTU201803907
- Lin, P. Y. (2014). 以半顯隱Runge-Kutta及擬譜法求解薛丁格方程 [master's thesis, National Chiao Tung University]. Airiti Library. https://doi.org/10.6842/NCTU.2014.00001
- 呂長和（2011）。四階有限差分的薛丁格波動方程解〔碩士論文，國立中正大學〕。華藝線上圖書館。https://www.airitilibrary.com/Article/Detail?DocID=U0033-2110201613495450
- Deng, G. J. (2017). 非線性薛丁格方程的基本理論及特殊解 [master's thesis, National Chiao Tung University]. Airiti Library. https://www.airitilibrary.com/Article/Detail?DocID=U0030-0705201811384635
- Wu, W. C. (2011). 薛丁格方程解在黎曼幾何上的分析 [master's thesis, National Tsing Hua University]. Airiti Library. https://doi.org/10.6843/NTHU.2011.00604