creeky belly
Posts: 205
Joined: June 2006
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I just redid the calculation, taking care to define an f = original wavefunction, g = complex conjugate, and h = f' (didn't have to, but I'm lazy with technology). Ignoring the root (r^4 must have been a screwup), I still came up with r<-constant. The problem is converting the hamiltonian
from position to momentum. I used Messiah's guidelines, which included an 'i' term, and squaring it I obtained the -1 which flipped the inequality. That's why the results still hold, at least when k = 0. |
In order to calculate the uncertainty, you need <r^2>-<r>^2, which I think is incalculable, since <r^2> will yield an infinite result. To find the uncertainty relation, you need <p^2>-<p>^2 as well. You will find that (<r^2>-<r>^2)(<p^2>-<p>^2) >= hbar/2.
| Quote | | In effect, I'm choosing different constants for different spaces, because the energies are not invariant across the "twist". In fact the twist changes the momentum, although this is only intuitive for now. |
I'm not sure what you mean by "twist", or what "information" really has to do with anything physical, but all the particle physics for the last century has supported the fact that, yes, the momentum/position distributions support both the Fourier relation and the Heisenberg uncertainty principle. I think you're starting to bark up your own tree here. You can't use your equations to support the logic, without some sort of physical consequence: i.e. if the constants are different in different spaces, then the distributions in each space should be off by your scale factor.
It's measurable; the problem is that it just doesn't happen the way you describe it.
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