Simple Harmonic Oscillator Zero Probability Points

In summary, the conversation discusses the physical meaning of zero probability in the Quantum SHO wave function and the concept of position in quantum mechanics. The experts suggest that the particle does not have a position unless we interact with it, and the zero points in the function indicate that the particle will not be found at those points. They also advise against discussing interpretations of quantum mechanics with beginners, as it may lead to confusion and unlearning of concepts.
  • #1
SSSUNNN
3
0
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?
 
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  • #2
SSSUNNN said:
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.
 
  • #3
Nugatory said:
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.
 
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Related to Simple Harmonic Oscillator Zero Probability Points

What is a Simple Harmonic Oscillator?

A Simple Harmonic Oscillator is a physical system that exhibits a periodic motion with a specific frequency, known as the natural frequency. This type of motion is characterized by a sinusoidal curve and can be found in various systems, such as a pendulum or a mass-spring system.

What are Zero Probability Points in a Simple Harmonic Oscillator?

Zero Probability Points, also known as Zero Crossing Points, are the points in a Simple Harmonic Oscillator's motion where the amplitude is zero. These points occur when the displacement of the oscillator is at its maximum or minimum, and the velocity is zero.

Why are Zero Probability Points important in a Simple Harmonic Oscillator?

Zero Probability Points are important because they help determine the behavior and properties of the oscillator. They can be used to calculate the amplitude and frequency of the oscillation, as well as the total energy and potential energy of the system.

How do Zero Probability Points affect the motion of a Simple Harmonic Oscillator?

The presence of Zero Probability Points in a Simple Harmonic Oscillator's motion results in a periodic and repetitive motion. The oscillator will continue to oscillate between these points, with its maximum velocity and acceleration occurring at these points.

What factors can affect the Zero Probability Points in a Simple Harmonic Oscillator?

The natural frequency, mass, and stiffness of the oscillator are the main factors that can affect the Zero Probability Points. A change in any of these factors can result in a change in the amplitude and frequency of the oscillation, thus affecting the location of the Zero Probability Points.

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