# Quantum mechanics,Taylor series and integrals

1. Mar 15, 2005

### eljose

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:

$$f(q,p)=\sum_0^{\infty}a_n(q)p^{n}$$

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

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

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

$$\int_0^{\infty}f(X)dx$$

is this justified or it cna not be done?..thanks.

2. Mar 15, 2005

### dextercioby

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.