Particle has certain energy levels in a potential well?

In summary, the 'Particle in a box' system follows certain energy levels due to the fact that it must obey the Schrodinger equation and there are boundary conditions. This is a consequence of quantum mechanics and the duality between particles and waves. It is our perception and metaphor that leads us to imagine behavior similar to everyday phenomena. However, after becoming familiar with quantum mechanics, one learns to appreciate its incredible power and success without worrying too much about the 'why' and 'how'.
  • #1
nickhobbs
In the 'Particle in a box' system, with the well being extremely narrow, why does the particle path have to follow certain energy levels compared to the classical system?

Thanks in advance.
 
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  • #2
Hello Nick, :welcome:

That's a direct consequence of 1. It has to obey the Schoedinger equation and 2. there are boundary conditions.

But now the original question shifts to: why does it have to obey the SE ? :smile:

That is Quantum mechanics for you. As the man sings: don't ask why
 
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  • #3
BvU said:
Hello Nick, :welcome:

That's a direct consequence of 1. It has to obey the Schoedinger equation and 2. there are boundary conditions.

But now the original question shifts to: why does it have to obey the SE ? :smile:

That is Quantum mechanics for you. As the man sings: don't ask why

Hi BvU, thanks for your answer! I understand that it has to obey the Schrodinger equation but it is also a consequence of wave-particle duality- and the quantum probability distribution shows it acts more like a wave at lower energy states?
 
  • #4
The duality you are referring to is our business. The particle has nothing to do with that: it is our perception we want to lean towards something from everyday experience. Little hard spheres or soft water waves to name two extremes. The 'thingy' (electron, photon, baseball, Jupiter) does not act. It is our metaphor for describing its behaviour that is deficient and lures us towards imagining behaviour that is characteristic for phenomena we know from daily life.

And don't worry -- everyone entering this strange world of quantum mechanics is looking for this kind of mental support. After a while you learn to enjoy the astounding power and success of this theory without worrying too much about the 'why' and 'how'.
 
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  • #5
BvU said:
The duality you are referring to is our business. The particle has nothing to do with that: it is our perception we want to lean towards something from everyday experience. Little hard spheres or soft water waves to name two extremes. The 'thingy' (electron, photon, baseball, Jupiter) does not act. It is our metaphor for describing its behaviour that is deficient and lures us towards imagining behaviour that is characteristic for phenomena we know from daily life.

And don't worry -- everyone entering this strange world of quantum mechanics is looking for this kind of mental support. After a while you learn to enjoy the astounding power and success of this theory without worrying too much about the 'why' and 'how'.

Ohh yeah, of course!
Thanks for the help!
 

1. What is a potential well?

A potential well is a region in space where a particle experiences a force that is directed towards the center of the well. This force creates a potential energy that is dependent on the position of the particle within the well.

2. How do energy levels in a potential well affect a particle?

The energy levels in a potential well determine the allowed energies that a particle can have while confined in the well. The particle can only occupy these discrete energy levels and cannot have energies in between them.

3. How does the shape of a potential well affect the energy levels of a particle?

The shape of a potential well affects the energy levels of a particle by determining the potential energy at different positions within the well. A deeper well will have lower energy levels, while a shallower well will have higher energy levels.

4. Can a particle have different energy levels in a potential well?

Yes, a particle can have different energy levels in a potential well. The allowed energy levels are determined by the quantum mechanical properties of the particle and the shape of the potential well.

5. How are the energy levels in a potential well related to the probability of finding a particle?

The energy levels in a potential well are related to the probability of finding a particle in a specific energy state. The higher the energy level, the lower the probability of finding the particle in that state. The lowest energy level, known as the ground state, has the highest probability of containing the particle.

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