Simple Harmonic Oscillator Zero Probability Points

[SSSUNNN]

Hi,
What is the physical meaning of zero probability of finding a particle in the square of the Quantum SHO wave function?
the particle is supposed to oscillate about the equilibrium position, how would it go from an end point to the other end point without passing by certain points?
Could the particle be transferred to another energy level that has a probability at these points when passing over these points?

 

[Nugatory]

Hi,
What is the physical meaning of zero probability of finding a particle in the square of the Quantum SHO wave function?
the particle is supposed to oscillate about the equilibrium position, how would it go from an end point to the other end point without passing by certain points?
Could the particle be transferred to another energy level that has a probability at these points when passing over these points?

No, the particle is not "passing over" these points. You're thinking that the particle is always somewhere (so it can't get from one place to another without moving through the space in between) and we just don't know where. That's not right, and letting go of that mental model has to be one of your first steps in learning quantum mechanics.

The particle has no position unless and until we interact with it in a way that allows us to determine its position. And we really do mean "no position", not "it's somewhere but we don't know where". When we aren't interacting with it to determine its position, it no more has a position than I have a lap when I'm not sitting down, or a fist when my hand is open.

The zero points in the function are telling us that no position measurement will ever find the particle at those points. And that's ALL they're telling us.

 

[ShayanJ]

The particle has no position unless and until we interact with it in a way that allows us to determine its position. And we really do mean "no position", not "it's somewhere but we don't know where". When we aren't interacting with it to determine its position, it no more has a position than I have a lap when I'm not sitting down, or a fist when my hand is open.

I don't think Demystifier likes that!

I don't want to criticize anything. I'm just wondering, is it really that we have to explain QM to beginners using Copenhagen? Can't we do it in an interpretation-neutral way?

I think we should make it clear for the beginners, that QM only gives probabilities for measurement outcomes and nothings else. Demanding more is wrong. Making the theory to give us more, means interpreting it in some way.
For beginners, we prefer not to talk about interpretations, so we should teach them not to ask more until they are skilled enough to learn about different interpretations and choose one. Otherwise they may want to unlearn some parts of their learning.