Sympy: substitute to symbolic bosonic commutation its numerical value










1














I would like to simplify expressions involving boson commutators using sympy.
The problem is that, using secondquant in sympy, the numerical values of the bosonic commutator [b_0,b^dagger_0]=1 and [b_0,b^dagger_1]=0 is never substituted to the symbolic expression.
In other words, I would like SymPy to know about the commutator identity.



The following code



from sympy import simplify
from sympy.physics.secondquant import Bd, B
from sympy.physics.quantum import *
comm1=simplify(Commutator(B(0),Bd(0)).doit())
print(comm1)
comm2=simplify(Commutator(B(0),Bd(1)).doit())
print(comm2)


gives



comm1= AnnihilateBoson(0)*CreateBoson(0) - CreateBoson(0)*AnnihilateBoson(0)
comm2= AnnihilateBoson(0)*CreateBoson(1) - CreateBoson(1)*AnnihilateBoson(0)


instead of the expected values:



comm1= 1
comm2= 0


I have tried the code mentioned here How to use sympy.physics.quantum Commutator?



comm2=(Commutator(B(0),Bd(0))._eval_expand_commutator()).doit()
print('comm2=',comm2)


but this gives the same expression as before



comm2= AnnihilateBoson(0)*CreateBoson(0) - CreateBoson(0)*AnnihilateBoson(0)


Moreover I have found this related unanswered question:
Does sympy give me wrong results for the second quantization commutators?



I had a look around line 1682 here:
https://github.com/sympy/sympy/blob/master/sympy/physics/secondquant.py
and according to this the commutator should correctly give a Kronecker delta. However, I still get the symbolic expression reported above.










share|improve this question




























    1














    I would like to simplify expressions involving boson commutators using sympy.
    The problem is that, using secondquant in sympy, the numerical values of the bosonic commutator [b_0,b^dagger_0]=1 and [b_0,b^dagger_1]=0 is never substituted to the symbolic expression.
    In other words, I would like SymPy to know about the commutator identity.



    The following code



    from sympy import simplify
    from sympy.physics.secondquant import Bd, B
    from sympy.physics.quantum import *
    comm1=simplify(Commutator(B(0),Bd(0)).doit())
    print(comm1)
    comm2=simplify(Commutator(B(0),Bd(1)).doit())
    print(comm2)


    gives



    comm1= AnnihilateBoson(0)*CreateBoson(0) - CreateBoson(0)*AnnihilateBoson(0)
    comm2= AnnihilateBoson(0)*CreateBoson(1) - CreateBoson(1)*AnnihilateBoson(0)


    instead of the expected values:



    comm1= 1
    comm2= 0


    I have tried the code mentioned here How to use sympy.physics.quantum Commutator?



    comm2=(Commutator(B(0),Bd(0))._eval_expand_commutator()).doit()
    print('comm2=',comm2)


    but this gives the same expression as before



    comm2= AnnihilateBoson(0)*CreateBoson(0) - CreateBoson(0)*AnnihilateBoson(0)


    Moreover I have found this related unanswered question:
    Does sympy give me wrong results for the second quantization commutators?



    I had a look around line 1682 here:
    https://github.com/sympy/sympy/blob/master/sympy/physics/secondquant.py
    and according to this the commutator should correctly give a Kronecker delta. However, I still get the symbolic expression reported above.










    share|improve this question


























      1












      1








      1


      1





      I would like to simplify expressions involving boson commutators using sympy.
      The problem is that, using secondquant in sympy, the numerical values of the bosonic commutator [b_0,b^dagger_0]=1 and [b_0,b^dagger_1]=0 is never substituted to the symbolic expression.
      In other words, I would like SymPy to know about the commutator identity.



      The following code



      from sympy import simplify
      from sympy.physics.secondquant import Bd, B
      from sympy.physics.quantum import *
      comm1=simplify(Commutator(B(0),Bd(0)).doit())
      print(comm1)
      comm2=simplify(Commutator(B(0),Bd(1)).doit())
      print(comm2)


      gives



      comm1= AnnihilateBoson(0)*CreateBoson(0) - CreateBoson(0)*AnnihilateBoson(0)
      comm2= AnnihilateBoson(0)*CreateBoson(1) - CreateBoson(1)*AnnihilateBoson(0)


      instead of the expected values:



      comm1= 1
      comm2= 0


      I have tried the code mentioned here How to use sympy.physics.quantum Commutator?



      comm2=(Commutator(B(0),Bd(0))._eval_expand_commutator()).doit()
      print('comm2=',comm2)


      but this gives the same expression as before



      comm2= AnnihilateBoson(0)*CreateBoson(0) - CreateBoson(0)*AnnihilateBoson(0)


      Moreover I have found this related unanswered question:
      Does sympy give me wrong results for the second quantization commutators?



      I had a look around line 1682 here:
      https://github.com/sympy/sympy/blob/master/sympy/physics/secondquant.py
      and according to this the commutator should correctly give a Kronecker delta. However, I still get the symbolic expression reported above.










      share|improve this question















      I would like to simplify expressions involving boson commutators using sympy.
      The problem is that, using secondquant in sympy, the numerical values of the bosonic commutator [b_0,b^dagger_0]=1 and [b_0,b^dagger_1]=0 is never substituted to the symbolic expression.
      In other words, I would like SymPy to know about the commutator identity.



      The following code



      from sympy import simplify
      from sympy.physics.secondquant import Bd, B
      from sympy.physics.quantum import *
      comm1=simplify(Commutator(B(0),Bd(0)).doit())
      print(comm1)
      comm2=simplify(Commutator(B(0),Bd(1)).doit())
      print(comm2)


      gives



      comm1= AnnihilateBoson(0)*CreateBoson(0) - CreateBoson(0)*AnnihilateBoson(0)
      comm2= AnnihilateBoson(0)*CreateBoson(1) - CreateBoson(1)*AnnihilateBoson(0)


      instead of the expected values:



      comm1= 1
      comm2= 0


      I have tried the code mentioned here How to use sympy.physics.quantum Commutator?



      comm2=(Commutator(B(0),Bd(0))._eval_expand_commutator()).doit()
      print('comm2=',comm2)


      but this gives the same expression as before



      comm2= AnnihilateBoson(0)*CreateBoson(0) - CreateBoson(0)*AnnihilateBoson(0)


      Moreover I have found this related unanswered question:
      Does sympy give me wrong results for the second quantization commutators?



      I had a look around line 1682 here:
      https://github.com/sympy/sympy/blob/master/sympy/physics/secondquant.py
      and according to this the commutator should correctly give a Kronecker delta. However, I still get the symbolic expression reported above.







      python physics sympy mathematical-expressions commutativity






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      edited Nov 12 '18 at 20:43

























      asked Nov 12 '18 at 19:57









      Caos

      16910




      16910






















          1 Answer
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          0














          The problem is caused by



          from sympy.physics.quantum import *


          This code gives the expected behaviour



          from sympy.physics.secondquant import *
          from sympy import symbols
          a, b = symbols('a,b')
          c = Commutator(B(a),Bd(a))
          print(c.doit())





          share|improve this answer




















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            1 Answer
            1






            active

            oldest

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            active

            oldest

            votes






            active

            oldest

            votes









            0














            The problem is caused by



            from sympy.physics.quantum import *


            This code gives the expected behaviour



            from sympy.physics.secondquant import *
            from sympy import symbols
            a, b = symbols('a,b')
            c = Commutator(B(a),Bd(a))
            print(c.doit())





            share|improve this answer

























              0














              The problem is caused by



              from sympy.physics.quantum import *


              This code gives the expected behaviour



              from sympy.physics.secondquant import *
              from sympy import symbols
              a, b = symbols('a,b')
              c = Commutator(B(a),Bd(a))
              print(c.doit())





              share|improve this answer























                0












                0








                0






                The problem is caused by



                from sympy.physics.quantum import *


                This code gives the expected behaviour



                from sympy.physics.secondquant import *
                from sympy import symbols
                a, b = symbols('a,b')
                c = Commutator(B(a),Bd(a))
                print(c.doit())





                share|improve this answer












                The problem is caused by



                from sympy.physics.quantum import *


                This code gives the expected behaviour



                from sympy.physics.secondquant import *
                from sympy import symbols
                a, b = symbols('a,b')
                c = Commutator(B(a),Bd(a))
                print(c.doit())






                share|improve this answer












                share|improve this answer



                share|improve this answer










                answered Nov 12 '18 at 21:18









                Caos

                16910




                16910



























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