Exploring Quantum Physics - Week 3 Question 3

Question:

Recall the definition of the parity operator $\hat{I}$ from lecture 5. What is $\hat{I}(xe^{-\frac{x^2}{2l^2}})$?

Answer:

This one is really simple, the operator does nothing but just substitute $x$ by $-x$, so we have the answer is $(-x)e^{-\frac{(-x)^2}{2l^2}} = -xe^{-\frac{x^2}{2l^2}}$