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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Almost periodic function and rotation number of the Schrodinger operator
薛定谔算子 几乎周期函数 旋转数
2023/4/25
The concept of almost periodic functions is due to H. Bohr. The concept of rotation number is due to H. Poincaré. The Schr?dinger operator is named after E. Schr?dinger. I will present our work relate...
The scaling limit of the critical one-dimensional random Schrodinger operator
critical one-dimensional random Schrodinger operator Probability
2011/9/9
Abstract: We consider two models of one-dimensional discrete random Schrodinger operators (H_n \psi)_l ={\psi}_{l-1}+{\psi}_{l +1}+v_l {\psi}_l, {\psi}_0={\psi}_{n+1}=0 in the cases v_k=\sigma {\omega...
Inverse Scattering for a Schrodinger Operator with a Repulsive Potential
Inverse scattering Repulsive potential
2007/12/11
We consider a pair of Hamiltonians $(H, H_0 )$ on $L^2 ({\Bbb R}^n ),$ where $H_0 = p^2 -x^2$ is a Schr\" odinger operator with a repulsive potential, and $H= H_0 +V(x)$. We show that, under suitable ...
Asymptotic Formulas for the Eigenvalues of the Schrodinger Operator
Asymptotic Formulas Schrodinger Operator
2010/3/1
In this paper, we obtain asymptotic formulas for the eigenvalues of the d-dimensional Schrodinger operator L=-D +q(x) in d-dimensional parallelepiped F with Dirichlet and Neumann boundary conditions.
Asymptotic Formulas for the Eigenvalues of the Schrodinger Operator
Asymptotic Formulas Schrodinger Operator
2010/3/1
In this paper, we obtain asymptotic formulas for the eigenvalues of the d-dimensional Schrodinger operator L=-D +q(x) in d-dimensional parallelepiped F with Dirichlet and Neumann boundary conditions.