Particle in Box: Zero Probability Density at Certain Points

In summary: ZapperZ said: "The probability density at certain points for a particle in a box is zero.Does this imply that the particle cannot move across these points"No, by saying that, you are assuming that you can track the particle's trajectory every step of the way. All the probability density says is that when you make a measurement, the probability of finding the particle at the nodes is zero.
  • #1
somebody-nobody
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The probability density at certain points for a particle in a box is zero.Does this imply that the particle cannot move across these points
 
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  • #2
somebody-nobody said:
The probability density at certain points for a particle in a box is zero.Does this imply that the particle cannot move across these points

No, because by saying that, you are assuming that you CAN track the particle's trajectory every step of the way. All the probability density says is that when you make a measurement, the probability of finding the particle at the nodes is zero.

Zz.
 
  • #3
somebody-nobody said:
The probability density at certain points for a particle in a box is zero.Does this imply that the particle cannot move across these points

Like ZapperZ said, the probability density merely defines where you can find the particle when you measure. To figure out if a particle will ever move in a spot of "zero", you should use the schrodinger equation.
 
  • #4
ZapperZ said:
No, because by saying that, you are assuming that you CAN track the particle's trajectory every step of the way. All the probability density says is that when you make a measurement, the probability of finding the particle at the nodes is zero.

Zz.
Yep. The proplem is with the question itself. The OP used the term move, which is a classical idea and not a quantum one. The question is better asked regarding what the probability of finding the particle in this region and then ask what the probability of measuring the particle in this other region after the first measurement was made. If the state is an eigenstate (stationary state) the the probability density will remain constant. But we really don't speak of measuring a particle in a region of zero width (i.e. what's the probability of finding the particle at x = 2?) because that will always be zero.

Pete
 

FAQ: Particle in Box: Zero Probability Density at Certain Points

1. What is a "Particle in a Box"?

A "Particle in a Box" refers to a theoretical model used in quantum mechanics to describe the behavior of a particle confined within a finite space. It assumes that the walls of the box are infinitely high and the particle has zero potential energy outside of the box.

2. What is meant by "Zero Probability Density" in the context of a Particle in a Box?

In a Particle in a Box system, the wave function of the particle can have areas with zero probability density. This means that there is no chance of finding the particle in those specific points within the box.

3. Why does a Particle in a Box exhibit zero probability density at certain points?

This phenomenon is a result of the wave nature of particles in quantum mechanics. The wave function of the particle can interfere with itself, causing certain points to have a cancellation of probability density, resulting in a zero probability of finding the particle at those points.

4. How does the size of the box affect the probability density of a Particle in a Box?

The size of the box directly affects the energy levels and probability density of a Particle in a Box. As the box size increases, the energy levels become more closely spaced and the probability density becomes more evenly distributed throughout the box.

5. Can a Particle in a Box have a non-zero probability density at every point?

No, a Particle in a Box cannot have a non-zero probability density at every point. This is because of the finite energy levels of the particle within the box. There will always be certain points with zero probability density due to the wave nature of the particle and the interference of its wave function.

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