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Introductory Physics Homework Help
Normalising superposition of momentum eigenfunctions
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[QUOTE="alec_grunn, post: 5506874, member: 568380"] Hi all, I asked for help with one part of this question [URL='https://www.physicsforums.com/threads/allowed-momentum-values-for-a-plane-wave.876438/']here[/URL]. But after thinking about another part of the question, I realized I didn't understand it as well as I'd thought. [h2]Homework Statement [/h2] Ψ(x,0)=A(iexp(ikx)+2exp(−ikx)) is a wave function. A is a constant. Can Ψ be normalised? [h2]Homework Equations[/h2] [code] ## {\langle}p{\rangle} = \Big( \sum_{n=1} \hbar C[SUB]n[/SUB] ^2) ## [/code] Where C[SUB]n[/SUB] [SUP]2[/SUP] is the probability that the associated momentum will be observed. [h2]The Attempt at a Solution[/h2] My initial thought was, plane waves can't be normalised, since that would violate the normalisation condition. But the equation above (from textbook 'foundations of modern physics'), implies one of two options in my mind. Either: 1) The wavefunction can be normalised by ## A= \frac{1}{\sqrt{5}} ## 2) The allowed momentum values are not ## p= ± \hbar k##, but ## p = ± \frac{\hbar k}{5A[SUP]2[/SUP]}## Both of these seem to have their own problems. The first because I've read in other places that plane waves can not be normalised (unless you have some a Fourier series which gives you a finite integral). And the second because the momentum should not vary due to its coefficient. Cheers, Alec [/QUOTE]
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Normalising superposition of momentum eigenfunctions
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