In this Homework you will prove the Heisenberg Uncertainty principle for the n=1 state of the particle in a box model. 

Q1

Find the expectation value of x for n=1 in a 1-d particle in the box with length L, and particle mass m.

Q2

Find the expectation value of x2 for n=1 in a 1-d particle in the box with length L, and particle mass m.

Q3

Find the expectation value of px for n=1 in a 1-d particle in the box with length L, and particle mass m.

Q4

Find the expectation value of p2x for n=1 in a 1-d particle in the box with length L, and particle mass m.

Using Δq2=?q2?-?q?2 and the expectation values you have now calculated, prove the Heisenberg Uncertainty principle holds true for the n=1 level of of the particle in the box.