1-D Quantum Mechanics Conceptual Problem

In summary, the discussion is about the concept of probability density for a particle in a box and its implications on the particle's movement. It is mentioned that the probability density can be graphed as |ψ|2 and there are points where the function is equal to zero, known as nodes. The question is whether these zero probability points indicate that the particle cannot move across them. The answer is no, as the particle can still cross these points, but the probability of finding it there is very low. This can be compared to a vibrating string, where the particle spends the shortest time at the points with the highest speed, resulting in a lower probability of being found there.
  • #1
Yosty22
185
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Homework Statement



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? Explain. (I found a picture online http://www.everyscience.com/Chemistry/Physical/Quantum_Mechanics/.images/PBxWvfns1.gif).

Homework Equations





The Attempt at a Solution



In a particle in a box, you can graph |ψ|2 is the probability of finding a particle at a certain point in space. If you graph the function, there are nodes where the function is equal to zero. I know that this implies that you will never find the particle at that specific location, and I also understand that the particle can still cross that node. I just cannot figure out a proper, physical way to explain this. I know that the answer is that these zero probability points do not imply that the particle cannot move across the points, but I am having trouble explaining why.

Any help would be great,
Thank you.
 
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  • #2
If it helps, imagine the particle as if connected to a vibrating string. It spends the shortest time in the vicinity of the point where its speed the highest is. The probability that you find the particle there is the lowest.

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Related to 1-D Quantum Mechanics Conceptual Problem

1. What is 1-D quantum mechanics?

1-D quantum mechanics is a branch of physics that deals with the behavior of particles in one-dimensional systems, such as a single atom or a particle moving along a straight line. It is based on the principles of quantum mechanics, which describe the behavior of particles at the atomic and subatomic level.

2. What is a conceptual problem in 1-D quantum mechanics?

A conceptual problem in 1-D quantum mechanics refers to a theoretical scenario or thought experiment that challenges our understanding of the behavior of particles in one dimension. These problems often involve paradoxes or counterintuitive outcomes that cannot be explained using classical physics.

3. How is 1-D quantum mechanics different from classical mechanics?

1-D quantum mechanics differs from classical mechanics in that it takes into account the wave-like nature of particles at the atomic level. In classical mechanics, particles are treated as discrete objects with definite positions and velocities, whereas in 1-D quantum mechanics, particles are described by wave functions that represent the probability of finding the particle at a certain position.

4. What are some real-world applications of 1-D quantum mechanics?

1-D quantum mechanics has many practical applications, such as in the development of electronic devices like transistors and lasers. It also plays a crucial role in understanding the behavior of atoms and molecules, which is essential in fields like chemistry and materials science.

5. How can conceptual problems in 1-D quantum mechanics be solved?

Conceptual problems in 1-D quantum mechanics can be solved by applying the principles and mathematical equations of quantum mechanics. These problems often involve using mathematical models and thought experiments to explore the behavior of particles in different scenarios and understanding the implications of quantum mechanics on their behavior.

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