- #1
- 2,810
- 605
Consider two hermitian operators A and B.
Imagine a system is in state [itex] |\psi\rangle [/itex],then we have:
[itex]
\langle \psi|[A,B]|\psi\rangle=\langle \psi|AB-BA|\psi\rangle=B^{\dagger}A^{\dagger}|\psi\rangle-BA|\psi\rangle=BA|\psi\rangle-BA|\psi\rangle=0
[/itex]
This just seems a little strange,for example we have [itex] [p,x]=-i \hbar [/itex] but the above statement says that [itex] \langle [p,x] \rangle=0 [/itex] which is strange because the average of a non-zero constant has become zero!
And also it does not give the uncertainty relations we know!
What's wrong?
Thanks
Imagine a system is in state [itex] |\psi\rangle [/itex],then we have:
[itex]
\langle \psi|[A,B]|\psi\rangle=\langle \psi|AB-BA|\psi\rangle=B^{\dagger}A^{\dagger}|\psi\rangle-BA|\psi\rangle=BA|\psi\rangle-BA|\psi\rangle=0
[/itex]
This just seems a little strange,for example we have [itex] [p,x]=-i \hbar [/itex] but the above statement says that [itex] \langle [p,x] \rangle=0 [/itex] which is strange because the average of a non-zero constant has become zero!
And also it does not give the uncertainty relations we know!
What's wrong?
Thanks