- 學位論文
在歐氏空間上薛丁格算子的熱核漸進展開
Heat kernel asymptotic expansions for Schrödinger operator on R^n
並列摘要
In this thesis, we study the expression of the heat kernel of the Schrodinger operator in Euclidean space and its asymptotic expansion. We start by observing the behavior of the constant coefficient Schr"odinger operator in Euclidean space and introduce the new symbol space, and write down the expression of the heat kernel by the approximation method. It's proved the existence and uniqueness of the heat kernel for the Schr"odinger operator in Euclidean space, and the asymptotic expansion of the heat kernel at time is approach to 0.
參考文獻
{1}R. Strichartz, A Guide To Distribution Theory and Fourier Transforms. Boca Raton, FL: CRC Press, 1994.
{2}Daniel Grieser, Notes on heat kernel asymptotics. Preprint, Available at http://www.staff.unioldenburg.de/daniel.grieser/wwwvortraege/vortraege.html.
延伸閱讀
- Hong, P. J. (2020). 哈里斯準則對淬火無序二維量子自旋系統的有效性 [master's thesis, National Taiwan Normal University]. Airiti Library. https://doi.org/10.6345/NTNU202000095
- Chen, J. H. (2010). 薛丁格方程的 Strichartz 估計與長波短波交互作用方程式的半古典極限 [master's thesis, National Chiao Tung University]. Airiti Library. https://doi.org/10.6842/NCTU.2010.00212
- Hsu, Y. C. (2007). 離散薛丁格方程的史特萊卡斯估計 [master's thesis, National Taiwan University]. Airiti Library. https://doi.org/10.6342/NTU.2007.02102
- Ateser, E., Ciftci, H., & Uğurlu, M. (2007). A Study of the Schrödinger Equation with the Linear Potential by the Asymptotic Iteration Method in 3D. Chinese Journal of Physics, 45(3), 346-351. https://www.airitilibrary.com/Article/Detail?DocID=05779073-200706-45-3-346-351-a
- Liu, M. C. (1973). Some asymptotic approximation theorems in real and complex analysis [doctoral dissertation, The University of Hong Kong]. Airiti Library. https://www.airitilibrary.com/Article/Detail?DocID=U0029-1812201200015327