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 — documentation:basics:eigen_states [2016/10/10 09:40] (current) 2016/10/06 20:36 Maurits W. Haverkort created 2016/10/06 20:36 Maurits W. Haverkort created Line 1: Line 1: + {{indexmenu_n>​5}} + ====== Eigen states ====== + ### + For a given operator ($H$) one can calculate the $N_{psi}$ lowest eigenstates with the function "​Eigensystem()"​. The function "​Eigensystem()"​ uses iterative methods and needs as an input a starting point. This either can be a set of wavefunctions or a set of restrictions. If "​Eigensystem()"​ is called with a set of starting functions the eigenstates found are those $N_{psi}$ with the lowest energy that have a nonzero matrix element of the operator $(H+1)^\infty$ with the starting state. + ​ + -- Eigenstates of the Lz operator ​ + -- starting from a wavefunction + NF=6 + NB=0 + IndexDn={0,​2,​4} + IndexUp={1,​3,​5} + psip = NewWavefunction(NF,​ NB, {{"​100000",​ math.sqrt(1/​2)},​ {"​000010",​ math.sqrt(1/​2)}}) + OppLz = NewOperator("​Lz",​ NF, IndexUp, IndexDn) + Eigensystem(OppLz,​psip) + ​ + You do not need to specify a set of starting functions, but can specify a set of starting restrictions. If you want to find the lowest 3 eigenstates with two electrons in the $p$ shell one can set restrictions such that all orbitals in the $p$ shell are included in the counting and the occupation should be minimal 2 and maximal 2. + ​ + -- Eigenstates of the Lz operator ​ + -- starting from a set of restrictions + NF=6 + NB=0 + IndexDn={0,​2,​4} + IndexUp={1,​3,​5} + OppLz = NewOperator("​Lz",​ NF, IndexUp, IndexDn) + StartRestrictions = {NF, NB, {"​111111",​2,​2}} + Npsi = 3 + psiList = Eigensystem(OppLz,​ StartRestrictions,​ Npsi) + ​ + ### + + + ### + alligned paragraph text + ### + + ===== Example ===== + + ### + description text + ### + + ==== Input ==== + ​ + -- some example code + ​ + + ===== Index ===== + - [[documentation:​basics:​basis|]] + - [[documentation:​basics:​operators|]] + - [[documentation:​basics:​wave_functions|]] + - [[documentation:​basics:​expectation_values|]] + - Eigen states + - [[documentation:​basics:​spectra|]] + - [[documentation:​basics:​resonant_spectra|]] + - [[documentation:​basics:​fluorescence_yield|]]