Many Particle in a one dimensional box

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Discussion Overview

The discussion centers on the behavior of five particles in a one-dimensional box, specifically exploring the wave functions, quantum superposition, entanglement, and the quantization of energy levels. The scope includes theoretical aspects of quantum mechanics and statistical mechanics.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant inquires about the nature of wave functions for five particles in a 1-D box and whether quantum superposition and entanglement would occur.
  • Another participant suggests that the discussion may involve statistical mechanics and raises questions about the distinguishability of the particles, their interactions, and the size of the box.
  • A participant proposes considering two cases: one with identical particles and another with distinguishable particles, while noting that elementary particles are treated as indistinguishable in quantum mechanics.
  • Links to external resources are provided to further explain the problem and related concepts.

Areas of Agreement / Disagreement

Participants express differing views on the treatment of particles as distinguishable or indistinguishable, and the implications of these distinctions on the system's behavior remain unresolved.

Contextual Notes

Limitations include assumptions about particle interactions, the size of the box, and the definitions of distinguishability and indistinguishability, which are not fully explored in the discussion.

dev70
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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 Schrödinger's Equation in a many particle 1-D box?
 
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You're crossing into the regime of statistical mechanics.

Are the particles distinguishable?
Do they interact? How?
How big is the box?
etc.
 
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.
 
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.
 

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