- 學位論文
薛丁格方程的Hamilton-Jacobi解法
The Hamilton-Jacobi Method Applied to the Schrodinger Equation
摘要
薛丁格方程的canonical formulation 在real symplectic space上被建構完成，則相對應的Hamilton-Jacobi equation 即可得到；接著再用Hamilton-Jacobi method將薛丁格方程的解解出。
關鍵字
薛丁格並列摘要
On a real symplectic space, the canonical formulation of the Schrodinger equa- tion is built, thereafter the associated Hamilton-Jacobi equation is established. The Schrodinger equation is thus solved by the Hamilton-Jacobi method.
參考文獻
[1] H. Goldstein, Classical Mechanics, 2nd edition, Addison-Wesley, 1980.
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[3] J.E. Marsden and T.S. Ratiu, Introductionto Mechanics and Symmetry, Springer Verlag,
[4] D. Musicki, Canonical transformations and the Hamilton-Jacobi method in the eld
[5] J. Parry, D. S. Salopek and J. M. Stewart, Solving the Hamilton-Jacobi equation for
延伸閱讀
- 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
- 張志銘（2012）。可微分函數的Hermite-Hadamard 型不等式的研究及其在某些特殊平均值的應用〔碩士論文，淡江大學〕。華藝線上圖書館。https://doi.org/10.6846/TKU.2012.00529
- Fan, Y. W. (2014). 柯西黎曼 Li-Yau-Hamilton 不等式即其應用 [doctoral dissertation, National Taiwan University]. Airiti Library. https://doi.org/10.6342/NTU.2014.01101
- Guan, J. K. (2014). Study of the Underlying Theory of the Nonlinear Schrodinger Equations [master's thesis, National Chiao Tung University]. Airiti Library. https://doi.org/10.6842/NCTU.2014.00275
- 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