Integral evaluation - mistake??

[littlepreston182]

Hi, everyone. I'm struggling with an integral evaluation - any help would be appreciated!

For starters, I'm trying to find the uncertainty in position of a particle in a carbon nanotube described by a specific wave function. More importantly, I've come across an integral evaluation which I just am not sure is correct. Here is the full calculation (which I've also attached):



My main question: if n is a positive integer, can the cos(2ax) term really be zero (which seems to be what the final product implies)? I can't find any situation where that term is zero (if n​ is a positive integer), or any situation in which I get the final product. Does anyone have any insight?


Thanks for the help!

 

[Ishuda]

cos(2ax)\(\displaystyle |_0^L\)=cos(2aL)-cos(0)=?

 

[littlepreston182]

Thanks!!

cos(2ax)\(\displaystyle |_0^L\)=cos(2aL)-cos(0)=?

And it's as simple as that...thank you for your help!

 

[Ishuda]

And it's as simple as that...thank you for your help!

You're welcome.