Uncertainty in particle position

[MaxJ]

Homework Statement

below

Relevant Equations

below

For this problem,

My solution is

However, the my answer for $\Delta x$ is not correct. The correct answer is $\Delta x = 0.18a$. Does someone please know what I have done wrong?

Kind wishes

 

[Orodruin]

what I have done wrong?

You have hand waved "zero by symmetry" where what you have waved away is not zero by symmetry. Why do you think it should be zero and what symmetry would there be?

 

[MaxJ]

You have hand waved "zero by symmetry" where what you hade waved away is not zero by symmetry. Why do you think it should be zero and what symmetry would there be?

Be blessed Sir.

I have doubt what you mean in regards to symmetry. Can you explain some more?

 

[Orodruin]

Be blessed Sir.

I have doubt what you mean in regards to symmetry. Can you explain some more?

You were the one trying to invoke symmetry arguments so you should be able to tell me why you think the integral should be zero "due to symmetry".