Particle has certain energy levels in a potential well?

[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.

 

[BvU]

Hello Nick,

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 ?

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

 

[nickhobbs]

Hello Nick,

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 ?

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 Schrödinger 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?

 

[BvU]

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'.

 

[nickhobbs]

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!