- #1

terp.asessed

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## Homework Statement

I read from a book (obtained from a library) which stated that:

"

*Wave patterns, no matter how complicated, can always be written as a sum of simple wave patterns.*

Ex: ψ(x) = sin"

Ex: ψ(x) = sin

^{2}x = 1/2 + cos2x/2I understand that ψ(x) has been decomposed with double angle trignometry formulas.

"

*More generally, it is possible to decompose the wave function into components corresponding to a constant pattern plus all possible wavelengths of hte form 2pi/n with n, an integer. That is, we can find coefficients c*

ψ(x) = sigma (n=0 to infinite) c"

_{n}such that:ψ(x) = sigma (n=0 to infinite) c

_{n}cos_{n}x In this ex, c_{0}= 1/2 and c_{2}= -1/2. All other coefficents are zero.So...since the statement said, "wave patterns, no matter how complicated," I decided to try out with ψ(x) = sin

^{4}x out of curiosity...

## Homework Equations

## The Attempt at a Solution

ψ(x) = sin

^{4}x

I used double angle formulas to get:

ψ(x) = (1-cos2x)

^{2}/4...meaning the wave pattern is decomposed into:

ψ(x) = 1/4 + cos2x/2 + cos

_{2}2x/4

However, I am trying to figure out about

*" Could someone explain how to use this method so that I can try it out on ψ(x) I just made up?*

"ψ(x) = sigma (n=0 to infinite) c

"ψ(x) = sigma (n=0 to infinite) c

_{n}cos_{n}x In this ex, c_{0}= 1/2 and c_{2}= -1/2. All other coefficents are zero.