Tiny question about potential wells

In summary, the probability distributions for the eigenfunctions in a potential well will have a specific number of anti-nodes, also known as maxima, depending on the quantum number that labels the states and energies. This means that for each energy level, there will be a corresponding number of maxima in the wave function. The image provided in the conversation may not work, but it is not necessary to understand this concept.
  • #1
Lisa...
189
0
Is it true that, no matter what, the number of tops the wave functions of the energy levels in a one dimensional potential well (like the one shown below) have is the same as the number of that energy level? I.e. does in every well the wavefunction have 1 top in E1, 2 in E2, 3 in E3 etc?

Potentialwell.GIF
 
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  • #2
Hi Lisa,

for a potential well it is true in general that the probability distributions for the eigenfunctions will have n anti-nodes where n is the quantum number that labels the states as well as the energies. I think this is what you mean by 'tops', as they will all be maxima. ie n = 1 has one maximum, n=2 has two and so forth.

ps i didn't look at the picture. either the link is broken or the computer I am on won't let me see it

gabe
 
  • #3
Hey there!

Thanks a bunch for your quick reply! It feels good to know I finally begin to understand a bit of these potential wells... And btw: I'm terribly sorry 'bout the picture! I already thought something went wrong... Oh well here's it again if you want to see it:

Potentialwell.GIF


Lisa

Ps Yeah I did mean maxima of the sine :blushing: I just couldn't come up with the correct English word for it fast :D In the Netherlands we call them 'toppen' (that's why I wrote tops) or 'buiken' (which literally means bellies). Of course the word maxima is used too, but not quite often. Perhaps it has something to do with the (crown)prinses from Argentina whose name is Maxima... :biggrin:
 

1. What is a potential well?

A potential well is a region in space where a particle is confined by a potential energy barrier. This means that the particle has a higher potential energy inside the well compared to outside, making it more likely to remain within the well.

2. How is a potential well created?

A potential well is created by applying an external potential energy to a particle. This can be done using electric or magnetic fields, or by creating a physical barrier. The shape and depth of the well depends on the strength of the potential energy applied.

3. How do particles behave in a potential well?

Particles in a potential well can either be bound within the well or have enough energy to escape. Bound particles oscillate back and forth within the well, while particles with enough energy will eventually leave the well. The behavior of particles in a potential well is governed by the laws of quantum mechanics.

4. What are some real-life applications of potential wells?

Potential wells have various applications in physics, chemistry, and engineering. They are used in particle accelerators, quantum computing, and in the study of atomic and molecular interactions. They are also important in designing efficient electronic devices such as transistors and diodes.

5. Can potential wells be manipulated or controlled?

Yes, potential wells can be manipulated and controlled using various methods. This includes changing the strength or shape of the potential energy barrier, applying external forces, or using quantum mechanical techniques to alter the behavior of particles within the well. This ability to control potential wells is crucial in many technological applications.

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