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Old Sep 19th 2015, 04:13 PM   #11
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Originally Posted by kiwiheretic View Post
Is that wavefunction even normalisable? Didn't we just talk about discarding solutions where psi doesn't tend to 0 as x tend to infinity in another thread?
I chose the signs on the exponentials carefully. I did an example integral on W|A here.

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Old Sep 19th 2015, 10:50 PM   #12
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Originally Posted by kiwiheretic
Isn't Schrodinger's equation postulated rather than derived?
That's correct. There are derivations of it in a certain sense of the term but they are only meant to be a rough outline of a derivation and not a real derivation because a real derivation is based on simpler postulates for which the Schrodinger equation "derivation" has none. It's really just a postulate.

Originally Posted by kiwiheretic
Besides, if psi is physical then what are its units? Does anyone even know?
The meaning of psi is that the norm of the normalized wavefunction is the probability density. Being a probability density it's not unitless. The units depend on the system and can be found by dimensional analysis just like topquark noted.

Originally Posted by kiwiheretic
I think Schrodinger once described it as some kind of energy density relation but wouldn't that imply it should be something like Joules per cubic metre or something?
I know of nowhere where he said that because its not true.

Originally Posted by kiwiheretic
Yet after all these years it continues to even defy definition!!
That's not true at all. The Shrodinger equation and the wave function psi are both well defined.

Originally Posted by kiwiheretic
What new revelations has psi unveiled about the internal structure of subatomic particles? Any? Or has it just been used to curve fit experimental data?

Last edited by Pmb; Sep 19th 2015 at 10:55 PM.
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Old Sep 19th 2015, 11:10 PM   #13
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Originally Posted by Pmb View Post

I know of nowhere where he said that because its not true.
From wikipedia:

The Schrödinger equation details the behavior of Ψ but says nothing of its nature. Schrödinger tried to interpret it as a charge density in his fourth paper, but he was unsuccessful.[20]:219 In 1926, just a few days after Schrödinger's fourth and final paper was published, Max Born successfully interpreted Ψ as the probability amplitude, whose absolute square is equal to probability density.[20]:220 Schrödinger, though, always opposed a statistical or probabilistic approach, with its associated discontinuities—much like Einstein, who believed that quantum mechanics was a statistical approximation to an underlying deterministic theory— and never reconciled with the Copenhagen interpretation.[21]
Ok, I admit my terminology accuracy was some what lacking but that is what I was referring to.
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Old Oct 7th 2016, 06:33 PM   #14
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This thread is old but I thought I would update it to highlight the current unsolved problem as I see it:

If you ask the fourier transform what transform of cos(t) is you will get sqrt(π/2) δ(w-1)+sqrt(π/2) δ(w+1). If you phase shift it with cos(t-a) and calculate the same transform you get sqrt(π/2) e^(i a) δ(w-1)+sqrt(π/2) e^(-i a) δ(w+1) and get the associated complex terms. Only the magnitude is constant because the magnitude of e^(- i a) = 1. So for all symmetrical (even) waveforms are not all the tranforms also real? If a phase shift in the transform only brings in an e^(-i a) factor of unity magnitude then what physical information (that would be otherwise unobtainable) do complex wave functions bring to the world of quantum mechanics observables? And can we assert that this information to be intrinsically unobtainable any other way other than by an appeal to complex numbers?

The potential function outlined by Topsquark earlier was a non even function, so my question may have been badly phrased. A better question might be "Can you give an example of a real valued psi location function, arising from a feasible real world schrodinger potential, that can't be simply corrected by a phase shift to give real solutions or the complex component isn't simply an e^(i * something) factor which disappears completely in the measurable magnitude (because it equals unity)?" (I wasn't clear on whether the finite potential well example satisfied this or not. Its easier for me to think about if I can see a picture of the waveform.)
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Old Oct 10th 2016, 05:48 AM   #15
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There seem to be a number of dimensions curled up in this thread.

1) PSI is describing a weird feature of reality (one that is difficult to reconcile with everyday macroscopic experience).
2) PSI includes complex terms that make it difficult to relate to any "real" physical quantity.

3) Are these complex terms a mathematical necessity, or could we (with sufficient additional effort) calculate PSI without involving complex terms?
4) If they are unavoidable, is the involvement of "imaginary" maths in some way integral to the weirdness of the quantum world?

5) Can a visualisable model of a (simple) PSI function be constructed so that we can poke it and thus get a more hands-on understanding of it...
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