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Can I define a relation between variables, such that the expression will also be evaluated (then assuming all indices are equal) when no index is given? $$ x_i + y_j = \delta_{ij} \stackrel{Mathematica\ recognizes \ then\ that}{\Rightarrow} x + y = \delta_{ii} = 1 $$ $$$$ $$$$

INITIAL QUESTION WAS: I define a relation for the annihilation and creation operator $a_i$ and $a_j$ like this $$[a_i, a_j^\dagger] = \delta_{ij}.$$

The commutator can be defined with the Quantum Notation package. I want to make the index ($i$, resp. $j$) optional, such that Mathematica recognizes that $$[a, a^\dagger] =1,$$ i.e. it assumes $i=j$ if no index is given. Is there a way to do this?

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    $\begingroup$ how do you currently define the relation? (for existing indices) $\endgroup$ – Pinguin Dirk Oct 4 '13 at 6:35
  • $\begingroup$ showing us your code could make things easier $\endgroup$ – Wizard Oct 4 '13 at 15:39
  • $\begingroup$ Dear Wizard, Dear Pinguin Dirk, I actually define the relation exactly like this $$[a_i, a_j^\dagger] = KroneckerDelta[ij],$$ since the Quantum Notation package supports commutator notation. I just asked out of curiosity, in the moment I am using the "double definition" (one time with and one time without indices) as swish suggested. $\endgroup$ – ahambi Oct 5 '13 at 18:10
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I have this package installed, so that's what I did, and everything worked:

enter image description here

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    $\begingroup$ Could you please 1) provide a link to the Quantum notation package and 2) edit in the real copyable code instead of the image? $\endgroup$ – István Zachar Feb 27 '14 at 12:08

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