Uncertainty principle (stationary state)

[nazmus sakib]

I have to derive

I did all the way but stuck with the ">=" to "=" sign. what is the logic behind it ? is it safe to write "approximate" while taking the square-root on both side ? or the energy term "V" has gone during the calculation so it has only momentum "p" ?

 

[vanhees71]

It should be a $\geq$ sign. Concerning the homework (you should post in the homework section!) think about what's the commutator between $\hat{x}$ and $\hat{H}$ and what it has to do with the general Heisenberg uncertainty relations for arbitrary pairs of observables!