Quantum Mechanics for Engineers |
|
© Leon van Dommelen |
|
D.35 The evolution of expectation values
To verify the stated formulae for the evolution of expectation values,
just write the definition of expectation value,
, differentiate to get
and replace
by ![$H\Psi$](img2975.gif)
on account of the Schrödinger
equation. Note that in the first inner product, the
appears in
the left part, hence comes out as its complex conjugate ![$\vphantom{0}\raisebox{1.5pt}{$-$}$](img47.gif)
.