If I have a solution to the time-dependent Schrodinger equation
[tex]
i \frac{\partial \psi(x,t)}{\partial t} = \left( -\frac 12 \Delta_x + V(x) \right) \psi(x,t)
[/tex]
and the potential is infinitely differentiable with compact support, then I know that [itex]\psi[/itex] has a continuous first derivative, right? In fact, doesn't the SECOND spatial derivative have to exist for this function, so that the first derivative also needs to be DIFFERENTIABLE? Or am I missing something?
[tex]
i \frac{\partial \psi(x,t)}{\partial t} = \left( -\frac 12 \Delta_x + V(x) \right) \psi(x,t)
[/tex]
and the potential is infinitely differentiable with compact support, then I know that [itex]\psi[/itex] has a continuous first derivative, right? In fact, doesn't the SECOND spatial derivative have to exist for this function, so that the first derivative also needs to be DIFFERENTIABLE? Or am I missing something?
via Physics Forums RSS Feed http://www.physicsforums.com/showthread.php?t=720118&goto=newpost
0 commentaires:
Enregistrer un commentaire