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Jan 25, 2012 at 19:15 vote accept countunique
Jan 25, 2012 at 16:45 comment added Maksim Zholudev @user19192, nothing happens to $\psi(x,t)$ here. You have wrong assumption that functions $\tilde\phi(p)$ and $\phi(p/\hbar)$ are equal. They differ by $\sqrt{\hbar}$ because the basis functions are also different. See the 2nd and 3rd formulas in the updated part of my answer.
Jan 25, 2012 at 16:40 history edited Maksim Zholudev CC BY-SA 3.0
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Jan 25, 2012 at 16:30 history edited Maksim Zholudev CC BY-SA 3.0
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Jan 25, 2012 at 16:06 comment added countunique I haven't studied bra-kets yet so I will have to save this to read later. But you are basically saying to just re-normalize the wave function? That makes notation tricky because then the $\psi(x,t)$ are no longer equal to themselves.
Jan 25, 2012 at 8:34 history edited Maksim Zholudev CC BY-SA 3.0
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Jan 25, 2012 at 8:29 history answered Maksim Zholudev CC BY-SA 3.0