- #1
karlzr
- 131
- 2
Consider two Hermitian operator A, B; Define
[A,B]=iC,
then operator C is also Hermitian.
we calculate the expectation value with respect to |a>, one eigenstate of A with the eigenvalue a.
From the left side, we have:
<a|[A,B]|a>=<a|(AB-BA)|a>=(a-a)<a|B|a>=0,
while on the right side, <a|iC|a> does not necessarily vanish.
That is :<a|[A,B]|a> ≠ <a|iC|a>, which is absurd !
So what is wrong in my calculation?
[A,B]=iC,
then operator C is also Hermitian.
we calculate the expectation value with respect to |a>, one eigenstate of A with the eigenvalue a.
From the left side, we have:
<a|[A,B]|a>=<a|(AB-BA)|a>=(a-a)<a|B|a>=0,
while on the right side, <a|iC|a> does not necessarily vanish.
That is :<a|[A,B]|a> ≠ <a|iC|a>, which is absurd !
So what is wrong in my calculation?