# Search results for: I. M. Sigal

Journal of Statistical Physics > 2018 > 172 > 2 > 458-476

*N*quantized electrons at positions

*x*

_{i}, and

*M*nuclei of charges

*Z*= (

*Z*

_{1},...,

*Z*

_{M}) fixed at positions

*y*= (

*y*

_{l},...,

*y*

_{M}). The Schrödinger Hamiltonian of such a system is given by ${H}_{Z,H}=\sum _{i=1}^{N}\left(-{\Delta}_{{x}_{i}}+{V}_{Coulomb}\left({x}_{i}\right)\right)+\frac{1}{2}\sum _{i\ne j}\frac{1}{\left|{x}_{i}-{x}_{j}\right|}$]]</EquationSource><EquationSource Format="TEX"><![CDATA[$${H_{Z,H}}...

Journal of Experimental and Theoretical Physics > 2017 > 125 > 1 > 123-137

^{2}V+U, λ=n

^{−1}, in the semiclassical limit in any number of dimensions. The potential V is non-negative, vanishing at infinity as 0(|x|−α),α>0, and forms a barrier about a compact region in which V has finitely many zeros. U∈L

_{loc}

^{2}is any real function which is bounded above and continuous except at...

Journal of Experimental and Theoretical Physics > 2016 > 123 > 1 > 119-126

Communications in Mathematical Physics > 2012 > 309 > 2 > 543-582

Communications in Mathematical Physics > 2009 > 291 > 1 > 151-176

*v*|| of the solitons, we show that, up to times of order ||

*v*|| after the collision, the solitons preserve their shape (in

*L*

^{2}-norm), and the dynamics of the centers of mass of the solitons is approximately determined by the external...

Communications in Mathematical Physics > 2008 > 283 > 3 > 613-646

Geometric and Functional Analysis > 2006 > 16 > 6 > 1377-1390

Journal of Statistical Physics > 2004 > 116 > 1-4 > 311-359

Letters in Mathematical Physics > 2000 > 53 > 4 > 313-320

Communications in Mathematical Physics > 2000 > 212 > 2 > 257-275

Communications in Mathematical Physics > 1999 > 201 > 3 > 549-576