Question

I have a wavefunction Ψ(x) and I am asked to:
find the value x for which the probability of finding the molecule is maximal.
-find the value x for which the probability of finding the molecule is minimal.
I'm having trouble with these questions, I know that I have to derive Ψ and find the zeros of the derivative but how do I know when they correspond to maxima or minima? And aren't the minima just the values for which Ψ*Ψ is zero?
Thank's in advance!

Answer 1

hello
you can get information about the maximal and the minimal of a function by its double differentiation
you just need to differentiate a function 2 times it means that you should differentiate the function that you get by differentiating the given function !
so if the value of the final obtatined function is less than zero , than the point is a minimal
and if itis +ve, then , the point is a maximal
now the question arises that if you get a finction of third degree, then what will you do???
you just need to put the point in the place of the variable (i.e. the root of the function where the value of the function is zero) and then solve it and get your answer by the above methods
i'm not too good at it
so you may even refer to this link for better understanding:
http://www.mathcentre.ac.uk/resources/uploaded/mc-ty-maxmin-2009-1.pdf

Answer 2

Recall that the probability of finding the molecule within dx is the
square of the wave function times dx. You are maximizing g(x) = psi(x)^2