- 17

- 0

In my textbook the explanation of the expectation value in general covering any observable [tex] Q [/tex] is:

[tex] \overline{Q} = \int \Psi^\ast (x,t) \hat{Q}\Psi(x,t) dx [/tex]

Then they define the commutator as:

[tex] [\hat{A},\hat{B}] = \hat{A}\hat{B}-\hat{B}\hat{A}[/tex]

Now for position and momentum they give directly it as:

[tex] [\hat{x},\hat{p}] = i\hbar[/tex]

Now my question is: how is that possible? I know what the operators of the observables for both position and momentum are, but I do not understand why the commutator can be derived trough the general form of EXPECTATION value?? Expectation value is a value but the commutator is an operator on operators??

Can anyone help me with this confusion? Im new to quantum physics. Thanx