What is a single particle state?

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Discussion Overview

The discussion revolves around the concept of single particle states in the context of statistical thermodynamics, particularly as it relates to a perfect quantal gas. Participants explore the meanings of occupation numbers, single particle states, and their implications in a simplified analogy.

Discussion Character

  • Conceptual clarification
  • Exploratory

Main Points Raised

  • One participant seeks clarification on the definitions of single particle states and occupation numbers, suggesting that occupation numbers represent the number of particles in a particular state.
  • Another participant confirms that each r state corresponds to a single particle with a specific energy, E_r.
  • A participant attempts to create a layman's analogy using balls in a box to illustrate the concept of states and occupation numbers.
  • One participant emphasizes that r is merely a label rather than a numerical value, comparing it to naming siblings.
  • Clarification is provided that if n3=100, it indicates 100 particles in the r=3 state, not just 3.
  • Discussion includes the idea that the state of a single particle is one of r possible states, and the overall state of the system is determined by the values of n_r and E_r.
  • One participant notes that in some quantum systems, the total number of particles is not fixed, as seen with photons, which can be annihilated.

Areas of Agreement / Disagreement

Participants generally agree on the basic definitions and concepts related to single particle states and occupation numbers, but there is some exploration of different interpretations and analogies. The discussion remains open-ended with no definitive conclusions reached.

Contextual Notes

Participants express varying levels of understanding and seek analogies to clarify complex concepts, indicating potential gaps in foundational knowledge. The discussion does not resolve all uncertainties regarding the implications of occupation numbers in different quantum systems.

quietrain
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i am studying thermodynamics statistically, and my textbook says for the perfect quantal gas, i have

r single particle states, and nr occupation numbers and Er single particle energies.


what do they mean?

occupation numbers are the number of particles in a particular state right? say n3 means 3 particles in the r=3 state? then with energies E3 ?

it gets confusing :( thanks
 
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I think you do understand. there are n_r particles in the r state, and each r state corresponds to a single particle with energy E_r.
 
is there some sort of analogy in laymans terms?

for example ,

in a box i have 10 balls

so what is a state? does it mean that in the state 1, i have 5 nike balls

so my occupation number is 5 for state 1.

so does it now mean that for state 2 , i can have all 10 balls be nike? so my occupation number is now 10?
 
I think that your problem is that you think of r as a number. But it is not really a number; it just a label, a name of something. For example, if you have three brothers, you may call them Jack, John and Jim; but you can also call them 1, 2 and 3, in the order of their birth. So r=1 means Jack, r=2 means John, and r=3 means Jim. Does it help?
 
quietrain said:
say n3 means 3 particles in the r=3 state?
No. For example, If n3=100, then it means 100 particles in the r=3 state.
 
The state of a single particle will be one of r possible single particle states.
The state of the system is determined by the values of each of the n_r and E_r.
In Layman's terms: in a given system, there will be a given number of balls of each brand.
 
oh...

so if i have 10 balls in a system

the sum of occupation numbers must be 10?

so let's say got 3 states, meaning blue black and green balls.

so when i say state r = blue, my occupation number is the number of blue balls?
 
Yes, you're right on both accounts.
Interestingly, some quantum systems don't require a fixed total number of particles (for example, photons can be annihilated), so in quantum mechanics, the sum of the occupation numbers is not necessarily a constant.
 
ah i see thanks everyone!
 

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