Summation Notation in QM

  • #1
knowwhatyoudontknow
27
5
Homework Statement:
Clarification of Summation index
Relevant Equations:
see below
I have a (trivial) question regarding summation notation in Quantum mechanics. Does

∑cnexp(iknx) = Ψ(x) imply that n ranges from -∞ to +∞ (i.e. all possible combinations of n)? i.e.
n

∑exp(iknx)
-∞

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(ikNx) -> sinx/cosx.

Just want to be absolutely sure. Thanks.
 

Answers and Replies

  • #2
PeroK
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Homework Statement:: Clarification of Summation index
Relevant Equations:: see below

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

∑cnexp(iknx) = Ψ(x) imply that n ranges from -∞ to +∞ (i.e. all possible combinations of n)? i.e.
n

∑exp(iknx)
-∞

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(ikNx) -> sinx/cosx.

Just want to be absolutely sure. Thanks.
The range of ##n## should be stated or clear from the context.
 

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