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—documentation:basics:eigen_states [2016/10/10 09:40] (current) – external edit 127.0.0.1
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 +{{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.
 +<code Quanty Example.Quanty>
 +-- 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)
 +</code>
 +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.
 +<code Quanty Example.Quanty>
 +-- 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)
 +</code>
 +###
 +
 +
 +###
 +alligned paragraph text
 +###
 +
 +===== Example =====
 +
 +###
 +description text
 +###
 +
 +==== Input ====
 +<code Quanty Example.Quanty>
 +-- some example code
 +</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|]]

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