Understanding the Probability Density of Psi in Quantum Mechanics

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In summary, my professor explained that the probability of finding a particle at a certain energy in a certain state is given by the wave function, but that sometimes a particle can get out of its potential well even if it has low energy by going through different dimensions.
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GTdan
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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?
 
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  • #2
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 :wink:
 
  • #3
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!)
 

What is quantum mechanics?

Quantum mechanics is a branch of physics that studies the behavior of particles at the atomic and subatomic level. It describes how particles such as electrons and photons behave and interact with each other.

What is the difference between classical mechanics and quantum mechanics?

Classical mechanics describes the behavior of macroscopic objects such as cars and planets, while quantum mechanics describes the behavior of particles on a much smaller scale. Classical mechanics follows the laws of Newtonian physics, while quantum mechanics follows the laws of probability and uncertainty.

What is quantum entanglement?

Quantum entanglement is a phenomenon where two or more particles become connected in such a way that the state of one particle is dependent on the state of the other, even if they are separated by large distances. This concept is a key component of quantum mechanics and has been confirmed through various experiments.

What is the Heisenberg uncertainty principle?

The Heisenberg uncertainty principle states that it is impossible to know both the exact position and momentum of a particle at the same time. This is due to the wave-like behavior of particles at the quantum level and the limitations of measurement tools.

How is quantum mechanics applied in real-world technologies?

Quantum mechanics has many practical applications in technologies such as transistors, lasers, and magnetic resonance imaging (MRI). It also plays a crucial role in the development of quantum computers, which have the potential to solve complex problems much faster than classical computers.

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