Differences

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--- cwf:coupled_system [2016/11/22 13:13] – markus
+++ cwf:coupled_system [2017/01/24 14:27] (current) – markus
@@ Line 29: / Line 29: @@
 \end{equation}
-Here $H_x = -\frac{\hbar^2}{2m}\Delta_x+V$ is the usual Hamiltonian with only the $x$-coordinates present and all terms with the potential $V$ have set $y=Y(t)$ after differentiation. Now we also notice that the given scheme is just the Taylor expansion of $\Psi(t,x,y)$ at $y=Y(t)$ (assumed to exist) and all orders together would give the full wave function $\Psi$ again. For this to hold it is imperative to check under which conditions a [[space-analyticity of wave function:|wave function is space-analytic]] and thus allows for a convergent Taylor series at arbitrary locations.
+Here $H_x = -\frac{\hbar^2}{2m}\Delta_x+V$ is the usual Hamiltonian with only the $x$-coordinates present and all terms with the potential $V$ have set $y=Y(t)$ after differentiation. Now we also notice that the given scheme is just the Taylor expansion of $\Psi(t,x,y)$ at $y=Y(t)$ (assumed to exist) and all orders together would give the full wave function $\Psi$ again. For this to hold it is imperative to check under which conditions a [[:cwf:space-analyticity of wave function:|wave function is space-analytic]] and, even more restrictive, allows for a convergent Taylor series with infinite radius of convergence at the location of the Bohmian trajectory $Y(t)$.