- 期刊
THE CAUCHY PROBLEM OF THE ONE DIMENSIONAL SCHRÖDINGER EQUATION WITH NON-LOCAL POTENTIALS
摘要
For a large class of operators A, not necessarily local, it is proved that the Cauchy problem of the Schrödinger equation: - d^2f(z)/dz^2 + Af(z) = s^2f(z), f(0)=0, f'(0)=1 possesses a unique solution in the Hilbert (H_2(Δ)) and Banach (H_1(Δ)) spaces of analytic functions in the unit disc Δ = {z: |z| ＜ 1}.
延伸閱讀
- Zhang, L., & Simos, T. E. (2016). An Efficient Numerical Method for the Solution of the Schrödinger Equation. Advances in Mathematical Physics, 2016(), 970-989. https://doi.org/10.1155/2016/8181927
- Deng, G. J. (2017). The Underlying Theory and Special Solutions of Nonlinear Schrödinger equation [master's thesis, National Chiao Tung University]. Airiti Library. https://www.airitilibrary.com/Article/Detail?DocID=U0030-0705201811384635
- Ye, Y. (2009). Self-Similar Solutions for Nonlinear Schrödinger Equations. Mathematical Problems in Engineering, 2009(), 824-838-49. https://doi.org/10.1155/2009/298980
- Yu, P. T. (2014). On the local-wellposedness of the Schrödinger equation [master's thesis, National Tsing Hua University]. Airiti Library. https://doi.org/10.6843/NTHU.2014.00336
- Zhao, Y., Cheng, D. F., & Yang, X. J. (2013). Approximation Solutions for Local Fractional Schrödinger Equation in the One-Dimensional Cantorian System. Advances in Mathematical Physics, 2013(), 85-89. https://doi.org/10.1155/2013/291386