I'm a bit puzzled about an excercise in which I have to find the expectation values for position and momentum. Normally this should be pretty easy but in this case I just don't get the point.
Wavefunction is: $$ \psi(x) = \frac{1}{\sqrt{w_0 \sqrt{\pi}}} e^{\frac{-(x-x_0)^2}{2(w_{0})^{2}}+ik_0 x} $$
In a) you have to find the momentum rep. of this and in b) they ask you to find the expectation values of position and momentum.
Normally I would just compute the integral but in the solution they state, that "By inspection, it is easy to see that the expectation values for position and momentum are: $x_0 $ and $\hbar k_0 $" and I really don't know how to find these values. If anyone could briefly explain what they meant with "easy" I would be really happy.
Best Answer
If you build the square of the wave function, the result is a gaussian curve. If you compare your result with the general form of a normal distribution you can see that x0 is the expectation value... http://en.wikipedia.org/wiki/Normal_distribution