Question

Suppose a beginning physics student asks you if it’s possible for a particle to be at two different places at the same instant in time. Use the Double-Slit
Experiment to answer the student’s question.

Details would be really helpful

Answer 1

Yes,it is possible to find a particle at two different positions with two different probabilities at the same time.

Explanations:

In the double slit experiment two point light sources interferes in such a way that at some points the resultant intensity is high (Constructive Interference) and at some points the resultant intensity is very low or zero (Destructive Interference ). Now if the sources are not point sources, if they have some finite dimension,(like source with finite radius) then the intensity differences between Constructive interference and destructive interference become low and at some finite dimension of the light sources we cannot distinguish the high and low intensity. We get uniform light intensity at the screen where light falls.

Now, in the case of particles we can see the same phenomenon, that at some points the probability of finding the particle is high and at some points the probability of finding the particle is low or zero. Now you may ask a question why in the real cases we could not see a particle at two or more different points. The answer is that in the real cases the particle is not a point particle or its dimension is not of the order of the distance between high and low probability region. As a result we cannot distinguish the high and low probability regions.(like the double slit experiment with finite dimension sources). Thus we get the particle's position at a particular single point where it hits. Also for the point particle with small velocity the distance between the high and low probability region is very very small so we cannot detect the high and low probability regions, we get a single point.