8275

7673

كارشناسي ارشد

رياضي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده رياضي

1392

هشت،77ص

ص.ع:به فارسي و انگليسي

منصور آقاسي

فريد بهرامي

25/09/1392

اسدالله رضوي، اعظم اعتماد

رياضي

ID7673

به فارسي و انگلسيي: قابل رويت در نسخه ديجيتال

Stifel and Grassmann manifolds in quantum chemistry Nona sadat Mahmoudi ns mahmoudi@math iut ac ir 2013 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr M Aghasi m aghasi@cc iut ac ir Advisor Dr F Bahrami fbahrami@cc iut ac ir 2010 MSC 22E65 58B20 Keywords Variational spaces in Hartree Fock theory Banach Lie group Homogeneous space Finsler manifold AbstractWe establish geometric properties of Stiefel and Grassmann manifolds which arise in relation to Slatertype variational spaces in many particle Hartree Fock theory and beyond In particular we provethat they are analytic homogeneous spaces and submanifolds of the space of bounded operators onthe single particle Hilbert space As a by product we obtain that they are complete Finsler mani folds These geometric properties underpin state ofthe art results on the existence of solutions toHartree Fock type equations To this we de ned the Stiefel manifold in quantum chemistry by CN 1 N H N i j L ij 1 i j N where N N typically the number of electrons is xed and H 1 H 1 R3 is the Sobolev space oforder one the single particle Hilbert space Let U CN be the unitary group of N N matrices The Grassmann manifold in quantum chemistry denoted by gN is de ned to be the quotient of theStiefel manifold under the equivalence relation N 1 N 1 N i Uij i j i 1Motivated by state of the art existence results on Hartree Fock type equations based on abstractcritical point theory the aim of this thesis is to establish the fundamental geometric properties and

منصور آقاسي

فريد بهرامي

اسدالله رضوي، اعظم اعتماد