Understanding the Probability Density of Psi in Quantum Mechanics

[GTdan]

I wasn't sure if I could ask this question in the other forum so I am posting it here. This is simply a qualitative question. I am taking an advanced Chemistry course that is all about quantum mechanics and some molecular physics. We were talking about the probability density of Psi.

I was always under the impression that the graph of this shows the probability of finding a particle at some energy in some state. But my professor said something about it tells all the places that the particle can be in that state. Then he said that (using the example of a particle in a box), a particle can get out regardless of its energy sometimes because it goes through different dimensions beyond the normal 3 or 4 we have.

I don't know, but I have never heard about particles flying through different dimensions before. Is it possible he explained it wrong or I heard wrong? I know for a fact he mentioned particles going through an 11th dimension but maybe he was talking about something else? Quantum Mechanics doesn't really predict this does it?

 

[Allday]

oh no!

Hi GTdan,

let me try to help here. Psi is the wave function. Let's work in ONE dimension to keep things simple. So, Psi is a function of x. If you take (Psi*)(Psi) you get the probability distribution. This will also be a function of x and will tell you where the particle has a chance of being if you make a measurement.

The weird thing is that if you try to enclose the particle in a potential well (the particle in a box) that the probability distribution has a non-zero value in places outside the box where it would classicaly be 0. This means the particle has a chance of tunneling through the potential barrier and getting out of the box. This doesn't involve travel in any extra spatial dimensions. Seems like who ever was teaching the course has been watching too many Brian Green specials

 

[GTdan]

See that's what I was thinking. Thanks for the explanation. I may have to be a bit skeptical of things in that class if it starts to sound a little off. (Sorry for the VERY slow response- my classes started to overwhelm me and I completely forgot I had posted this topic!)