# Particle in an infinite well.

## Main Question or Discussion Point

we're learning about some of the properties of the steady state wave functions confined in an infinite well. one of the properties was that the steady state wave functions are "complete". and we're learning how to find the coefficient c(n) that "weights" each steady state solution in finding the general solution.

http://i.imgur.com/p0Ewvx8.jpg

can someone please explain to me what exactly i'm doing in the integral in order to find c(n)?

first of all, why am i even doing anything with ψ(m)*? ie how does the 'ψ(m)' come into play? what IS it?? is it just another steady state wave function?

so then in the end is this saying that the coefficient for the nth steady state solution is equal to the steady state solution of ... the orthogonal steady state ψ(m)?..

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jtbell
Mentor
To understand what's happening here, it might help to pretend that there are only a small number of steady-state wave functions, say 4 instead of ∞, then choose a value of m (i.e. one particular coefficient cm to evaluate) and write out the sum explicitly.

i understand the part where the other values go to zero, i'm more confused with the bigger picture; the coefficient c(n) is associated with the steady state psi(n). so what does any other function have to do with c(n)? i just don't understand the role of another function with c(n)

WannabeNewton