Physical significance of nodes?

[Sheldon Cooper]

Hi,

II have an issue with nodes in QM, like suppose in a well, the number of nodes depend on (n-1), the thing is that, what is so special(physically) about the point that the particle cannot be located there?

Thanks is advance

 

[Nugatory]

the thing is that, what is so special(physically) about the point that the particle cannot be located there?

Nothing is special about those points. You can make any point be a node or not be a node just by changing the energy of the particle, which tells us that it's the energy that matters and not some properties of the points in space where the nodes happen to be.

An analogy from classical physics: A planet will pass through some points in space and not others as it moves around the sun. That doesn't make the points along the orbit special; the planet is just going where Newton's laws say it will go and not going anywhere else.

 

[nashed]

Nothing is special about those points. You can make any point be a node or not be a node just by changing the energy of the particle, which tells us that it's the energy that matters and not some properties of the points in space where the nodes happen to be.

An analogy from classical physics: A planet will pass through some points in space and not others as it moves around the sun. That doesn't make the points along the orbit special; the planet is just going where Newton's laws say it will go and not going anywhere else.

While I do agree that nodes aren't special, I think you're mistaken about the energy bit, you can always refine a Hamilton by adding cI where I is unity and c is a real constant, this will change all observable energies by c but will not alter the eigenbasis, that is energy is not unique, basis are

 

[Nugatory]

While I do agree that nodes aren't special, I think you're mistaken about the energy bit, you can always refine a Hamilton by adding cI where I is unity and c is a real constant, this will change all observable energies by c but will not alter the eigenbasis, that is energy is not unique, basis are

Yes, that's right... I could have said $p^2$ to be more accurate.

 

[Jilang]

Perfect cancellation of right moving and left moving waves.