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

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ZapperZ

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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.
 
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