Position of particle in infinite potential well

In summary, the conversation discusses calculating the probability of finding a particle in a specific region within an infinite potential well for different energy levels. The classical result is compared to the calculated probabilities for n=1 and n=8, with the conclusion that classically the probability is 1/2. The person also requests clarification on how this situation is modeled classically.
  • #1
Froskoy
27
0

Homework Statement


For the case n=1, calculate the probability that the particle is found in within the region a/4<x<3a/4 (n is the energy level, a is the width of the infinite potential well). Compare this result with the case n=8 and with the classical result.


Homework Equations


Schrödinger equation.


The Attempt at a Solution


I've calculated the probabilities for n=1 and n-8 by integrating the square of the probability amplitude over the required region. I'm totally confused by comparing it to the classical result, though. I'm not sure what this is asking? Classically, would there be an equal probability of finding the particle anywhere, so this would just be 0.5?
 
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  • #2
That's right. Classically, the probability is 1/2.
 
  • #3
Why? Please can you point me to somewhere that explains how this situation is modeled classically?
 

Related to Position of particle in infinite potential well

1. What is the "infinite potential well" in particle physics?

The infinite potential well is a theoretical concept used in particle physics to represent a system where a particle is confined to a finite space with an infinitely high potential at the boundaries. This is often used to study the behavior of particles in a confined space, such as an atom or a solid state material.

2. How is the position of a particle in an infinite potential well determined?

The position of a particle in an infinite potential well is determined by the Schrödinger equation, which is a mathematical equation used to describe the quantum state of a system. The wave function solution of this equation gives the probability of finding the particle at a certain position inside the well.

3. What is the significance of the "particle in a box" model?

The "particle in a box" model, also known as the infinite potential well, is a simplified version of real-world particle systems that allows scientists to study the behavior of particles in a confined space. It has been used to understand the properties of atoms, electrons in semiconductors, and other quantum systems.

4. How does the size of an infinite potential well affect the energy levels of a particle?

The size of an infinite potential well directly affects the energy levels of a particle. As the size of the well increases, the energy levels become closer together, meaning that the particle has more possible energy states. Conversely, as the size decreases, the energy levels become more discrete, with fewer possible energy states for the particle.

5. Can a particle escape from an infinite potential well?

No, a particle cannot escape from an infinite potential well. Due to the infinitely high potential at the boundaries, the particle is confined within the well and cannot leave. However, the particle can tunnel through the potential barrier, which is a quantum mechanical phenomenon where the particle has a small probability of appearing outside of the well.

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