I have a problem with the argument of a finite square well.
The stuff I read has mentioned that the Curvature " second derivative " is opposite sign of the wave function only when the E larger than V where E = energy of the particle V = potential.This is how we obtained oscillatory solution (when E is larger than V) ( I understood this part )
And For E smaller than V ,it is true that we obtain exponential solutions, but can we use the same argument I used above? Is it true that as u = ( exp(-ikx ) decays the curvature has the same sign, so the negative gradient starts getting to be more positive but less and less positive until it tails down to infinity? since now second derivative u depends on the value of u and the difference between E and V.
Is it a correct way of interpreting this phenomena?
Appreciate any idea or help from every one.