The flux-across-surfaces theorem for short range potentials and wave functions without energy cutoffs
The flux-across-surfaces theorem for short range potentials and wave functions without energy cutoffs
复制标题
无能量截止的短程势和波函数的跨面通量定理
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
K. Münch
中科院分区：
文献类型：
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作者：
S. Teufel;D. Dürr;K. Münch
粒子随时间和远处表面积分的量子概率流给出了粒子在某个时间穿过该表面的概率。这些交叉概率与通常的散射截面公式之间的关系是由通量跨面定理提供的，该定理是由Combes、牛顿和Shtokhamer[Phys]猜想的。修订本D 11,366-372(1975)]。我们证明了无能量截断的短程势和波函数的跨表面通量定理。这一证明是基于自由跨表面通量定理(Daumer等人)。让我们来看看。数学课。太棒了。38,103-116(1996)]，以及广义本征函数的光滑性：证明了如果势V(X)像|x|−γ一样在无穷远处随γ>；n∈N衰减，则相应的哈密顿−1/2Δ+V的广义本征函数关于动量变量是n−2次连续可微的。
The quantum probability flux of a particle integrated over time and a distant surface gives the probability for the particle crossing that surface at some time. The relation between these crossing probabilities and the usual formula for the scattering cross section is provided by the flux-across-surfaces theorem, which was conjectured by Combes, Newton, and Shtokhamer [Phys. Rev. D 11, 366–372 (1975)]. We prove the flux-across-surfaces theorem for short range potentials and wave functions without energy cutoffs. The proof is based on the free flux-across-surfaces theorem (Daumer et al.) [Lett. Math. Phys. 38, 103–116 (1996)], and on smoothness properties of generalized eigenfunctions: It is shown that if the potential V(x) decays like |x|−γ at infinity with γ>n∈N then the generalized eigenfunctions of the corresponding Hamiltonian −1/2Δ+V are n−2 times continuously differentiable with respect to the momentum variable.