Quote:
Originally Posted by ballaratdragons
Fred,
the sigmoid curve speed function can be extended and smoothed with little, but useful, distortion of the curve but the 3N-dimensional configuration must be balanced thus:
i \hbar {\partial \over \partial t} \Psi(x_1,...,x_n,t) = \hbar^2 (-{\nabla_1^2\over 2m_1} - {\nabla_2^2 \over 2m_2} ... - {\nabla_N^2\over 2m_N} ) \Psi(x_1,...,x_n,t) + V(x_1,..,x_n,t)\Psi(x_1,...,x_n,t). \,
but to be Time independent, you cannot use Rally's suggestion of Y-c = (x-b)/sqrt(1+(x-b)^2).
To be Time independent AND achieve proper smooth transitions between speed steps this must be the resultant configuration:
\psi_{-|E|}(x) = C_1 e^{\sqrt{2m|E|/\hbar^2}\,x} + C_2 e^{-\sqrt{2m|E|/\hbar^2}\,x}.\,
If you end up with a backwash effect from any form of Time dilation you will need to run a discrete delta potential method scenario to test it.
Here is how:
Φ(s) = ∑ G(s,ai)V(ai)Φ(ai) + γ(s)
Good luck.
Glad to see you have plenty of time on your hands to attempt this project 
With all this rain, I suppose there's not much else to do  |
I think I just stepped into an agument in a Greek Bar ...
