Does Summation Over n from -∞ to +∞ in Quantum Mechanics Equal Ψ(x)?

[knowwhatyoudontknow]

Homework Statement

Clarification of Summation index

Relevant Equations

see below

I have a (trivial) question regarding summation notation in Quantum mechanics. Does

∑c_nexp(ik_nx) = Ψ(x) imply that n ranges from -∞ to +∞ (i.e. all possible combinations of n)? i.e.
ⁿ
_∞
∑exp(ik_nx)
^-∞

I believe it does to be consistent with the Fourier series in terms of complex exponentials.
n = 1 to +∞ would then be used when exp(ik_Nx) -> sinx/cosx.

Just want to be absolutely sure. Thanks.

 

[PeroK]

Homework Statement:: Clarification of Summation index
Relevant Equations:: see below

I have a (trivial) question regarding summation notation in Quantum mechanics. Does

∑c_nexp(ik_nx) = Ψ(x) imply that n ranges from -∞ to +∞ (i.e. all possible combinations of n)? i.e.
ⁿ
_∞
∑exp(ik_nx)
^-∞

I believe it does to be consistent with the Fourier series in terms of complex exponentials.
n = 1 to +∞ would then be used when exp(ik_Nx) -> sinx/cosx.

Just want to be absolutely sure. Thanks.

The range of $n$ should be stated or clear from the context.