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Quantum mechanics,Taylor series and integrals

  1. Mar 15, 2005 #1
    Let,s suppose we have the operator f(q,p) with p and q are quantum operators tehn my question is if we develop f(p,q) into a power series:

    [tex]f(q,p)=\sum_0^{\infty}a_n(q)p^{n}[/tex]

    my question is if i must symmetrizy the expresion a_n(q)p^n for each member
    so:

    [tex]a_n(q)p^n\rightarrow[a_n(q),p^n] [/tex]

    another question let be the integral of the operator x given by:

    [tex]\int_0^{\infty}f(X)dx [/tex]

    is this justified or it cna not be done?..thanks.
     
  2. jcsd
  3. Mar 15, 2005 #2

    dextercioby

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    To the second question,I don't see the connection between X & "x".To the first,yes,if they anticommute,they must be symmetrized wrt all possible equivalent classical combinations.The outcome,an operatorial function,must be self-adjoint,just like the inputs.

    Daniel.
     
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