| Schr(o|¨)dinger equations are the basic equations of the Quantum Mechanics, which havegreat theoretical significance in mathematics and quantum theory. At present, many prob-lems about Schr(o|¨)dinger equations already have lots of international works,such as uniquecontinuation of solutions, spectral analysis, self-adjiont properties and so on. The study ofgeneral Schr(o|¨)dinger equations is relatively mature, which not only has unique continuationof solutions of second order high dimensional and high order one-dimensional Schr(o|¨)dingerequations with constant coefficients, but also obtain sufficient conditions on a solution andthe potential V, which guarantee the unique continuation of solutions of Schr(o|¨)dinger equa-tions with variable coefficient through Hardy’s uncertainty principles.However, the study ofgeneralized Schr(o|¨)dinger equations is developing.Based on the theory of general Schr(o|¨)dinger equations, the paper talks about uniquecontinuation of solutions of generalized Schr(o|¨)dinger equations. The paper is composed ofthree chapters.In chapter one, we introduce some basic theory, major marks and inequality.In chapter two, we prove unique continuation of solutions of generalized linearSchr(o|¨)dinger equations with variable coefficients in a neighborhood of zero. At first, weexchange the form of Carleman estimate through decompressing solidification method andorthogonal transformation. Then, we hunt a suitable G to obtain deformed Carleman esti-mate. Finally, we obtain the unique continuation of solutions of Schr(o|¨)dinger equations in aneighborhood of zero by above Carleman estimate.In chapter three, by orthogonal transformation, Calderón estimate and energy estimate,we obtain the exponential decay estimate and the L~2Carleman estimate with weight.Then, we talks about unique continuation of solutions of generalized Schr(o|¨)dinger equationswith constant coefficients in Rnby the result in chapter two and above results in this chapter. |
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