I'm enjoying this introductory essay about quantum mechanics found here(adsbygoogle = window.adsbygoogle || []).push({});

http://www4.ncsu.edu/unity/lockers/users/f/felder/public/kenny/papers/psi.html

and I have a question. About five-eighths of the way into it a wave function is given "at time t=0",

[tex]

\psi = \sqrt { \frac {2} {L} } [ \frac {1}{2} sin (\pi x / L) + \frac { \sqrt {3} }{2} i sin (5 \pi x / L)]

[/tex]

and some questions and answers follow. If I am understanding the authors, the answers imply that this wavefunction is a (normalized) linear combination of two momentum eigenfunctions, where the momenta are [itex] h/2L [/itex] and [itex] 5h/2L [/itex].

My question is, shouldn't

[tex]

\psi = \sqrt { \frac {2} {L} } [ \frac {1}{2} (cos (\pi x / L) + i sin (\pi x / L)) + \frac { \sqrt {3} }{2} (cos (5 \pi x / L)

+ i sin (5 \pi x / L))]

[/tex]

or - more succinctly -

[tex]

\psi = \sqrt {\frac {2} {L} } [ \frac {1}{2} e ^ {i \pi x / L } + \frac { \sqrt {3} } {2} e ^ {i 5 \pi x / L } ]

[/tex]

?

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# About momentum eigenfunctions

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