Many Particle in a one dimensional box

In summary, the conversation discusses the system of keeping 5 particles in a 1-D box and how this affects the wave functions, quantum superposition, entanglement, and energy levels. It also delves into solving the Schrodinger's Equation in a many particle 1-D box and the considerations for distinguishable particles and different box lengths. The concept of indistinguishable elementary particles in quantum mechanics is also mentioned. A link is provided for further understanding of the problem.
  • #1
dev70
58
0
Hi pf,

I am just wondering how would the system be if i keep say 5 particles in a 1-D box. How would the wave functions be? Will quantum superposition happen? Entanglement? What about the energy levels? How would they be quantized? In short i want to know how would you solve the Schrodinger's Equation in a many particle 1-D box?
 
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  • #3
You're crossing into the regime of statistical mechanics.

Are the particles distinguishable?
Do they interact? How?
How big is the box?
etc.
 
  • #4
What if we consider two cases in which particles are identical and other in which they are not (distinguishable )? And as far as the box is considered, we may take any length say 'a' but in one dimension only.
 
  • #5
dev70 said:
What if we consider two cases in which particles are identical and other in which they are not (distinguishable )? And as far as the box is considered, we may take any length say 'a' but in one dimension only.

Elementary particles are treated as indistinguishable in quantum mechanics, provided that they are of the same type.

Did you follow the link that I posted? It explains the problem well.
 

Related to Many Particle in a one dimensional box

1. What is a one dimensional box in the context of many particle systems?

A one dimensional box is a theoretical model in which particles are confined to a one-dimensional space, similar to a particle being trapped in a one-dimensional container. This model is often used to study the behavior of particles in a confined space, such as in nanotechnology or condensed matter physics.

2. What is the significance of studying many particle systems in a one dimensional box?

The study of many particle systems in a one dimensional box can provide insights into the behavior of particles in confined spaces, which has practical applications in nanotechnology and materials science. It also serves as a simplified model for understanding more complex systems, such as atoms in a molecule or electrons in a solid state material.

3. How are energy levels and wave functions related in a one dimensional box?

In a one dimensional box, the energy levels of particles are quantized, meaning they can only have certain discrete values. The corresponding wave functions for each energy level describe the probability of finding a particle at a specific location within the box.

4. What is the relationship between the size of the box and the energy of the particles?

The size of the box has a direct impact on the energy levels of particles within it. As the box size decreases, the energy levels become more closely spaced, and the energy of the particles increases. Conversely, as the box size increases, the energy levels become more widely spaced, and the energy of the particles decreases.

5. How does the number of particles affect the behavior of a one dimensional box system?

The behavior of a one dimensional box system is greatly influenced by the number of particles present. As more particles are added, the energy levels become more closely spaced and the overall energy of the system increases. This results in a higher probability of particles occupying higher energy levels and a more complex wave function for the system.

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