Integers n and m: Does the Sum of Sines Equal Zero?

[Xkaliber]

If n and m are integers and L is a positive number, does this equal zero?

$$\frac{sin(\frac{n\pi}{L}-\frac{m\pi}{L})}{\frac{n\pi}{L}-\frac{m\pi}{L}}-\frac{sin(\frac{n\pi}{L}+\frac{m\pi}{L})}{\frac{n\pi}{L}+\frac{m\pi}{L}}$$

 

[quasar987]

if m=n, this expression is not defined because the first denominator is 0.

Otherwise, it depends on what L, m and n are.

If you want to know if your equation is valid for any n,m, L whatever, try a numerical counter-exemple: plug say L=1.3, m=1, n=4.

 

[Xkaliber]

Since sin(n*Pi) = 0 only when n is an integer, in my previous case, it depends on the value of L, correct?

 

[Xkaliber]

Thanks. That's what I was afraid of. I am actually trying to show that a certain wave function is properly normalized and needed this to be 0 to have the correct answer. I'll move this discussion over to the physics subforum.