====== DensityMatrix ======
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//DensityMatrix(psi, OrbitalTable, options)// creates the density matrix of psi $a^{\dagger}_{\tau}a^{\phantom{\dagger}}_{\tau'}$ for the orbitals included in orbitaltable. It returns a table.
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===== Input =====
* psi : Wavefunction or a list of wavefunctions
* OrbitalTable : Vector (table) of unsigned integers. Orbitals start at 0. If the table is not given, all orbitals will be included.
* options: a list of options. Currently, only one option can be given: { {"Tensor", bool} }, where bool can be true or false. This option can be used when a list of wavefunctions are given. If the option is set to true, the density matrix is taken with respect to all wavefunctions $\langle \psi_{n} | a^{\dagger}_{\tau}a^{\phantom{\dagger}}_{\tau'} | \psi_{n'} \rangle $. The default value is false, where those density matrices with $n = n'$ will be calculated. The output will be a matrix of density matrices.
===== Output =====
* rho : Matrix (Table of Tables) of reals of dimension #OrbitalTable
===== Example =====
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description text
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==== Input ====
dofile("../definitions.Quanty")
print("For the wave-function")
print(psi1)
print("the density matrix is")
rho = DensityMatrix(psi1)
print(rho)
print("the density matrix of orbital 1 and 4 is (counting starts at 0)")
rho = DensityMatrix(psi1,{1,4})
print(rho)
==== Result ====
For the wave-function
WaveFunction: Wave Function
QComplex = 0 (Real==0 or Complex==1)
N = 2 (Number of basis functions used to discribe psi)
NFermionic modes = 6 (Number of fermions in the one particle basis)
NBosonic modes = 0 (Number of bosons in the one particle basis)
# pre-factor Determinant
1 9.486832980505E-01 100010
2 3.162277660168E-01 110000
the density matrix is
{ { 1 , 0 , 0 , 0 , 0 , 0 } ,
{ 0 , 0.1 , 0 , 0 , 0.3 , 0 } ,
{ 0 , 0 , 0 , 0 , 0 , 0 } ,
{ 0 , 0 , 0 , 0 , 0 , 0 } ,
{ 0 , 0.3 , 0 , 0 , 0.9 , 0 } ,
{ 0 , 0 , 0 , 0 , 0 , 0 } }
the density matrix of orbital 1 and 4 is (counting starts at 0)
{ { 0.1 , 0.3 } ,
{ 0.3 , 0.9 } }
===== Table of contents =====
{{indexmenu>.#1}}