Periodic potential V(x) -- how can I show that the period is d?

[GAB1]

periodic potential

how can i show that period is d

 

[ZapperZ]

View attachment 233240periodic potential

View attachment 233241
how can i show that period is d

for cos (2πx/d), change the values of x in terms of d, i.e. 0.1d, 0.2d ... etc... When do you get the full cycle?

BTW, this is math, not physics.

Zz.

 

[RPinPA]

If $f(x)$ has a period of $d$ then $f(x) = f(x + d)$ for all $x$.

Change $x$ to $x + d$. See what happens.

I should note that this only establishes the $d$ is a period. If you shift a sine wave of period $T$ by 10 periods, you get the same sine wave, so $10T$ is a period but not the smallest period. You have to do a little more reasoning to establish that $d$ is the smallest period.

 

[Mark44]

Thread closed as the OP has been banned.