How can be possible that a particle can be at two places but not in the middle?

Question

When solving the schrodinger equation for a monodimensional box, and making Ψ^2 i could find that for n=2 the probability to find the particle between 0 and L is at L/4 and 3L/4 but, it cant be found in L/2.....it's kinda weird, i'd like to know what happens exactly in this case comparing to the first energy level. Is this gonna happen if i keep raising n?

Answer 1

I'm no physicist. I answer Philosophy, R&S, and History.

But Ayn Rand said it is "epistemology which sets the standards for the special sciences."

When a special science comes up with such an idea as one particle in two places and not in the middle, the epistemology being used is obviously faulty.

I believe that in the end, when the answer to your question is solved, it will be found that the particle cannot be in two places at the same time.

In deductive logic there are precisely 256 forms of syllogism. Of these only 15 are valid (24 if you use Aristotle's categories.) So in such a complicated science as physics, it would be extremely easy to mistake one of the 241 forms of invalid conclusions as being valid. We often make the same type of mistake just in the act of speaking, let alone in complicated math.

Answer 2

That's because it isn't a particle as you are used to thinking of one, but instead is a "sort-of" particle with wave-like properties.  The amplitude of the wave is the probability of finding the "particle".  The probability is zero when the wave function goes through a node.

That's why it is called the Schroedinger wave equation.