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documentation:tutorials:introduction_to_quanty:wavefunctions [2016/10/07 20:23] – created Maurits W. Haverkortdocumentation:tutorials:introduction_to_quanty:wavefunctions [2025/11/20 03:29] (current) – external edit 127.0.0.1
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 +{{indexmenu_n>4}}
 +====== Wavefunctions ======
  
 +###
 +The fourth example creates wave-functions.
 +###
 +
 +###
 +<code Quanty Wavefunctions.Quanty>
 +-- We start with the same basis as before
 +NF=6
 +NB=0
 +IndexDn={0,2,4}
 +IndexUp={1,3,5}
 +
 +-- We now can create wave functions. For this we 
 +-- need three inputs:
 +-- (1) The number of Fermions and Bosons
 +-- (2) A list defining the wavefunctions. The lists
 + -- consists of a string defining a determinant by
 + -- its occupation: (1 occupied, 0 empty). One bit
 + -- for each fermion, 8 bit for a boson (i.e. a 
 + -- boson can have an occupation between 0 and 255).
 +-- (3) A number giving the pre-factor of the 
 +-- determinant.
 +psi0=NewWavefunction(NF, NB, {{"100000",math.sqrt(1/2)}, {"000001",math.sqrt(1/2)}})
 +
 +-- We can print the function
 +print(psi0)
 +
 +-- The name of the wave function is generic, we can
 +-- set it
 +psi0.Name = "psi 0"
 +print(psi0)
 +
 +-- We now could create all one electron functions 
 +-- in the basis of the p-shell.
 +psi0=NewWavefunction(NF,NB,{{"100000",1}})
 +psi0.Name = "psi(1 -1 1/2 -1/2)"
 +psi1=NewWavefunction(NF,NB,{{"001000",1}})
 +psi1.Name = "psi(1  0 1/2 -1/2)"
 +psi2=NewWavefunction(NF,NB,{{"000010",1}})
 +psi2.Name = "psi(1  1 1/2 -1/2)"
 +psi3=NewWavefunction(NF,NB,{{"010000",1}})
 +psi3.Name = "psi(1 -1 1/2  1/2)"
 +psi4=NewWavefunction(NF,NB,{{"000100",1}})
 +psi4.Name = "psi(1  0 1/2  1/2)"
 +psi5=NewWavefunction(NF,NB,{{"000001",1}})
 +psi5.Name = "psi(1  1 1/2  1/2)"
 +
 +-- And print them
 +print("============================")
 +print(psi0)
 +print(psi1)
 +print(psi2)
 +print(psi3)
 +print(psi4)
 +print(psi5)
 +print("============================")
 +
 +-- The wavefunctions should be orthonormal, we can 
 +-- easily test this
 +psiList={psi0,psi1,psi2,psi3,psi4,psi5}
 +for i = 1, 6 do
 +  for j = 1, 6 do
 +    print("<",psiList[i].Name," | ", psiList[j].Name," > =",psiList[i] * psiList[j])
 +  end
 +end
 +print("============================")
 +-- in table or matrix form:
 +psiList={psi0,psi1,psi2,psi3,psi4,psi5}
 +for i = 1, 6 do
 +  for j = 1, 6 do
 +    io.write(string.format("%3i ",psiList[i] * psiList[j]))
 +  end
 +  io.write("\n")
 +end
 +</code>
 +###
 +
 +###
 +The output is:
 +<file Quanty_Output Wavefunctions.out>
 +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   7.071067811865E-01       100000
 +   2   7.071067811865E-01       000001
 +
 +
 +
 +WaveFunction: psi 0
 +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   7.071067811865E-01       100000
 +   2   7.071067811865E-01       000001
 +
 +
 +============================
 +
 +WaveFunction: psi(1 -1 1/2 -1/2)
 +QComplex         =          0 (Real==0 or Complex==1)
 +N                =          1 (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   1.000000000000E+00       100000
 +
 +
 +
 +WaveFunction: psi(1  0 1/2 -1/2)
 +QComplex         =          0 (Real==0 or Complex==1)
 +N                =          1 (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   1.000000000000E+00       001000
 +
 +
 +
 +WaveFunction: psi(1  1 1/2 -1/2)
 +QComplex         =          0 (Real==0 or Complex==1)
 +N                =          1 (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   1.000000000000E+00       000010
 +
 +
 +
 +WaveFunction: psi(1 -1 1/2  1/2)
 +QComplex         =          0 (Real==0 or Complex==1)
 +N                =          1 (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   1.000000000000E+00       010000
 +
 +
 +
 +WaveFunction: psi(1  0 1/2  1/2)
 +QComplex         =          0 (Real==0 or Complex==1)
 +N                =          1 (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   1.000000000000E+00       000100
 +
 +
 +
 +WaveFunction: psi(1  1 1/2  1/2)
 +QComplex         =          0 (Real==0 or Complex==1)
 +N                =          1 (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   1.000000000000E+00       000001
 +
 +
 +============================
 +< psi(1 -1 1/2 -1/2) | psi(1 -1 1/2 -1/2) > = 1
 +< psi(1 -1 1/2 -1/2) | psi(1  0 1/2 -1/2) > = 0
 +< psi(1 -1 1/2 -1/2) | psi(1  1 1/2 -1/2) > = 0
 +< psi(1 -1 1/2 -1/2) | psi(1 -1 1/2  1/2) > = 0
 +< psi(1 -1 1/2 -1/2) | psi(1  0 1/2  1/2) > = 0
 +< psi(1 -1 1/2 -1/2) | psi(1  1 1/2  1/2) > = 0
 +< psi(1  0 1/2 -1/2) | psi(1 -1 1/2 -1/2) > = 0
 +< psi(1  0 1/2 -1/2) | psi(1  0 1/2 -1/2) > = 1
 +< psi(1  0 1/2 -1/2) | psi(1  1 1/2 -1/2) > = 0
 +< psi(1  0 1/2 -1/2) | psi(1 -1 1/2  1/2) > = 0
 +< psi(1  0 1/2 -1/2) | psi(1  0 1/2  1/2) > = 0
 +< psi(1  0 1/2 -1/2) | psi(1  1 1/2  1/2) > = 0
 +< psi(1  1 1/2 -1/2) | psi(1 -1 1/2 -1/2) > = 0
 +< psi(1  1 1/2 -1/2) | psi(1  0 1/2 -1/2) > = 0
 +< psi(1  1 1/2 -1/2) | psi(1  1 1/2 -1/2) > = 1
 +< psi(1  1 1/2 -1/2) | psi(1 -1 1/2  1/2) > = 0
 +< psi(1  1 1/2 -1/2) | psi(1  0 1/2  1/2) > = 0
 +< psi(1  1 1/2 -1/2) | psi(1  1 1/2  1/2) > = 0
 +< psi(1 -1 1/2  1/2) | psi(1 -1 1/2 -1/2) > = 0
 +< psi(1 -1 1/2  1/2) | psi(1  0 1/2 -1/2) > = 0
 +< psi(1 -1 1/2  1/2) | psi(1  1 1/2 -1/2) > = 0
 +< psi(1 -1 1/2  1/2) | psi(1 -1 1/2  1/2) > = 1
 +< psi(1 -1 1/2  1/2) | psi(1  0 1/2  1/2) > = 0
 +< psi(1 -1 1/2  1/2) | psi(1  1 1/2  1/2) > = 0
 +< psi(1  0 1/2  1/2) | psi(1 -1 1/2 -1/2) > = 0
 +< psi(1  0 1/2  1/2) | psi(1  0 1/2 -1/2) > = 0
 +< psi(1  0 1/2  1/2) | psi(1  1 1/2 -1/2) > = 0
 +< psi(1  0 1/2  1/2) | psi(1 -1 1/2  1/2) > = 0
 +< psi(1  0 1/2  1/2) | psi(1  0 1/2  1/2) > = 1
 +< psi(1  0 1/2  1/2) | psi(1  1 1/2  1/2) > = 0
 +< psi(1  1 1/2  1/2) | psi(1 -1 1/2 -1/2) > = 0
 +< psi(1  1 1/2  1/2) | psi(1  0 1/2 -1/2) > = 0
 +< psi(1  1 1/2  1/2) | psi(1  1 1/2 -1/2) > = 0
 +< psi(1  1 1/2  1/2) | psi(1 -1 1/2  1/2) > = 0
 +< psi(1  1 1/2  1/2) | psi(1  0 1/2  1/2) > = 0
 +< psi(1  1 1/2  1/2) | psi(1  1 1/2  1/2) > = 1
 +============================
 +  1   0   0   0   0   0 
 +  0   1   0   0   0   0 
 +  0   0   1   0   0   0 
 +  0   0   0   1   0   0 
 +  0   0   0   0   1   0 
 +  0   0   0   0   0   1 
 +</file>
 +###
 +
 +===== Table of contents =====
 +{{indexmenu>.#1|msort}}

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