- #1
p2bne
- 3
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Hi all, i cannot find where's the trick in this little problem:
We have an hermitian operator A and another operator B, and let's say they don't commute, i.e. [A,B] = cI (I is identity). So, if we take a normalized wavefunction |a> that is eigenfunction of the operator A so that A|a> = a|a>, we should have
<a|[A,B]|a> = c.
But if i write
<a|AB|a> - <a|BA|a>
and, since A is hermitian, i make it act on the bra for the first term and on the ket for the second one i get
a<a|B|a> - a<a|B|a> = 0.
I really don't see where is the problem...
Homework Statement
We have an hermitian operator A and another operator B, and let's say they don't commute, i.e. [A,B] = cI (I is identity). So, if we take a normalized wavefunction |a> that is eigenfunction of the operator A so that A|a> = a|a>, we should have
<a|[A,B]|a> = c.
But if i write
<a|AB|a> - <a|BA|a>
and, since A is hermitian, i make it act on the bra for the first term and on the ket for the second one i get
a<a|B|a> - a<a|B|a> = 0.
I really don't see where is the problem...