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documentation:basics:eigen_states [2016/10/10 09:40] (current)
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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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