====== Problems with creation and annihilation operators ======
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asked by [[mailto:camjjr.cm@gmail.com|Carlos Alberto Martins Junior]] (2020/02/22 18:59)
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<WRAP center box 100%>
Hello,

I am trying to learn how to program using Quanty, however I am having some issues to understand why my code is wrong. I tried to print the creation and annihilation operators in a d shell basis but the result is wrong. My code is

<code>
NF=10
NB=0


IndexDn={0,2,4,6,8}
IndexUp={1,3,5,7,9}

psi0 =NewWavefunction(NF,NB,{{"0000000000",1}})
psi1 =NewWavefunction(NF,NB,{{"1000000000",1}})
psi2 =NewWavefunction(NF,NB,{{"1100000000",1}})
psi3 =NewWavefunction(NF,NB,{{"1110000000",1}})
psi4 =NewWavefunction(NF,NB,{{"1111000000",1}})
psi5 =NewWavefunction(NF,NB,{{"1111100000",1}})
psi6 =NewWavefunction(NF,NB,{{"1111110000",1}})
psi7 =NewWavefunction(NF,NB,{{"1111111000",1}})
psi8 =NewWavefunction(NF,NB,{{"1111111100",1}})
psi9 =NewWavefunction(NF,NB,{{"1111111110",1}})
psi10=NewWavefunction(NF,NB,{{"1111111111",1}})


psilist={psi0,psi1,psi2,psi3,psi4,psi5,psi6,psi7,psi8,psi9,psi10}

OppN   = NewOperator("Number",NF,{0,1,2,3,4,5,6,7,8,9,10},{0,1,2,3,4,5,6,7,8,9,10},{1,1,1,1,1,1,1,1,1,1,1})
OppCr  = NewOperator("Cr",NF,{0,1,2,3,4,5,6,7,8,9,10},{1,1,1,1,1,1,1,1,1,1,1})
OppAn  = NewOperator("An",NF,{0,1,2,3,4,5,6,7,8,9,10},{1,1,1,1,1,1,1,1,1,1,1})



print("Operator N:")
for i=1,11 do
 for j=1,11 do
  io.write(string.format("%5.2f",psilist[i]*OppN*psilist[j]))
  end
  io.write("\n")
end
print("")
	
print("Operator Cr:")
for i=1,11 do
 for j=1,11 do
  io.write(string.format("%5.2f",psilist[i]*OppCr*psilist[j]))
  end
  io.write("\n")
end
print("")

print("Operator An:")
for i=1,11 do
 for j=1,11 do
  io.write(string.format("%5.2f",psilist[i]*OppAn*psilist[j]))
  end	
  io.write("\n")
end
print("")

</code>

And my result is 

<code>
Operator N:
 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
 0.00 0.00 2.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
 0.00 0.00 0.00 3.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
 0.00 0.00 0.00 0.00 4.00 0.00 0.00 0.00 0.00 0.00 0.00
 0.00 0.00 0.00 0.00 0.00 5.00 0.00 0.00 0.00 0.00 0.00
 0.00 0.00 0.00 0.00 0.00 0.00 6.00 0.00 0.00 0.00 0.00
 0.00 0.00 0.00 0.00 0.00 0.00 0.00 7.00 0.00 0.00 0.00
 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 8.00 0.00 0.00
 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 9.00 0.00
 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0010.00

Operator Cr:
 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
 0.00-1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
 0.00 0.00 0.00-1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00
 0.00 0.00 0.00 0.00 0.00-1.00 0.00 0.00 0.00 0.00 0.00
 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00
 0.00 0.00 0.00 0.00 0.00 0.00 0.00-1.00 0.00 0.00 0.00
 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00
 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00-1.00 0.00

Operator An:
 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
 0.00 3.61-1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
 0.00 0.00 5.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
 0.00 0.00 0.00 6.08-1.00 0.00 0.00 0.00 0.00 0.00 0.00
 0.00 0.00 0.00 0.00 7.00 1.00 0.00 0.00 0.00 0.00 0.00
 0.00 0.00 0.00 0.00 0.00 7.81-1.00 0.00 0.00 0.00 0.00
 0.00 0.00 0.00 0.00 0.00 0.00 8.54 1.00 0.00 0.00 0.00
 0.00 0.00 0.00 0.00 0.00 0.00 0.00 9.22-1.00 0.00 0.00
 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 9.85 1.00 0.00
 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0010.44-1.00
 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0011.00
</code>


I do not understand why I got this result for the creation and annihilation operators. 
   
</WRAP>

~~DISCUSSION|Answers~~