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

AI Thread Summary
To demonstrate that the period of a periodic potential V(x) is d, one can analyze the function f(x) and show that f(x) = f(x + d) for all x. By substituting x with x + d, the periodicity can be confirmed. However, establishing that d is the smallest period requires additional reasoning, as larger multiples of d can also satisfy the periodic condition. The discussion emphasizes the mathematical nature of the problem rather than a physical interpretation. Ultimately, the thread concludes with the note that the original poster has been banned.
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periodic potential

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how can i show that period is d
 

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GAB1 said:
View attachment 233240periodic potential

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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.
 
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.
 
Thread closed as the OP has been banned.
 
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