Potential Wells: What Is a Potential Well & What Does Its Graph Tell Us?

[Shaybay92]

So I have looked up some related posts about potential wells but none of them really actually talk about what a potential well IS... what does the line on the graph actually tell us? what potential is it talking about?

 

[Drakkith]

Got a link to a graph to show us by chance?

 

[Shaybay92]

http://en.wikipedia.org/wiki/File:Potential_well.png
Something like this... but its not really this exact example. I just want to know how you go from a physical situation (e.g. an electron going past a proton) to a potential well diagram.

 

[Drakkith]

http://en.wikipedia.org/wiki/File:Potential_well.png
Something like this... but its not really this exact example. I just want to know how you go from a physical situation (e.g. an electron going past a proton) to a potential well diagram.

Ohh...I wish i knew enough to help you out. I don't know either though.

 

[ShayanJ]

At first we calculate the potential of every point of space.In fact we make a scalar field.
Then we draw a diagram of potential vs. position.
A potential well in fact is somewhere which a particle is in equilibrium.How do we understand it?
The point is that in a potential field,force arrows are toward the decrease of potential.so a particle placed in a potential field always moves to reach the point with less potential.A potential well has the least potential in an area of the field.So a particle stays there till its applied a force.If a force is not big enough to move it out of well,it starts to oscillate about the minimum and at last stops at that point.
And one point.A potential well is not only in quantum mechanics.Its in classical physics too.
I hope I helped

 

[Shaybay92]

Hi Shyan, thanks so much.

Now I have another question, if we have a potential well diagram as I showed above and there is a particle with more energy than the top of the well, why is it that we know for sure it won't go into that well. I mean, as you said there are forces causing this potential well so why won't this particle be pushed towards the well?... I hope this makes sense.

 

[ShayanJ]

A particle has a total energy shown by E and E=U+K
K is the particle's kinetic energy and U potential energy which is derived from the potential of the particle's position and one of the particle's properties for example its charge.In this case U=qV.
When the forces acting on the particle are just conservative forces(electromagnetism and gravity),E is conserved.So U or K can't get bigger than E.this is the meaning of that dashed horizontal line.In your diagram,the particle can't go further than x1 and x2 because beyond those points,U>E.
If the force creating the field is the only force acting on the particle,just this force affects its motion.Another possibility for this situation is drawing the field for the net force acting on the particle(providing all forces are conservative because just conservative forces have force and potential fields)
Looks like I didn't understand your question but I think I gave you enough information for answering it still feel free asking more!I'll be happy.

 

[Zero?]

This is a little off topic but can anyone explain to me how to sketch a wave function based on the potential well without having to solve the Schrödinger Equation? Apparently for a triangular potential well the solution looks like http://www.nextnano.de/nextnano3/tutorial/1Dtutorial_GaAs_triangular_well.htm . My problem is the question I'm doing asks me to sketch it simple arguments without doing any calculations. Anyone have any clue how to justify it without referring to the Airy functions? I understand that the wavefunction will be greater near the low potential but how do i justify it more articulately?

Btw can anyone explain how a particle can escape a finite well even when its total energy is less than the well itself? Is it just a consequence of having part of the wavefunction lie outside the well?