What exactly is a quantum state?

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Discussion Overview

The discussion centers around the concept of a quantum state, particularly its definition and implications in quantum mechanics, with references to Bose-Einstein Condensate and the Pauli Exclusion Principle. Participants explore the differences between quantum and classical states of a system.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant questions the meaning of a quantum state and its relation to Bose-Einstein Condensate and the Pauli Exclusion Principle.
  • Another participant attempts to clarify that the state of a physical system is a mathematical object from which observable properties can be derived, contrasting classical and quantum states.
  • A further contribution notes that in quantum mechanics, the state is represented as a vector in Hilbert space, while also mentioning that technically, it is a (unit) ray in most axiomatizations.
  • One participant expresses concern that the mathematical subtleties may be beyond the original poster's current understanding, suggesting a lack of advanced study in the subject.
  • A participant reveals their educational level, indicating they are in 7th grade, which raises questions about the appropriateness of the technical discussion.
  • Another participant reiterates the point about the state being a (unit) ray, while also addressing the potential for perceived nitpicking in the discussion.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the concept of a quantum state, with some technical disagreements about the mathematical representation. There is no consensus on the clarity of the concept for the original poster.

Contextual Notes

The discussion highlights limitations in understanding complex mathematical concepts related to quantum states, particularly for participants with less advanced educational backgrounds.

quantum.cmptr
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What is a quantum state of a system? I keep hearing it, but I'm not able to fully understand what it means, especially in relation to Bose-Einstein Condensate, and the Pauli Exclusion Principle.
 
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quantum.cmptr said:
What is a quantum state of a system? I keep hearing it, but I'm not able to fully understand what it means, especially in relation to Bose-Einstein Condensate, and the Pauli Exclusion Principle.
Do you know what a classical state of a system is?
 
No, I do not.
 
quantum.cmptr said:
No, I do not.
In general, the state of physical system is a mathematical object(s) in terms of which all observable properties of the system can be calculated. In classical physics the state of the system is a point in phase space; the coordinates and the corresponding momenta. In quantum mechanics, the state of the system is a vector in an abstract vector space called the Hilbert space. In general, given the state of the physical system at some initial time, the equations of the theory tell you what the state will look like in a later time.
 
Technically, in most axiomatizations, a state is a (unit) ray, not a vector. But this mathematical subtlety is far beyond our OP's current level of understanding, as I suspect he's not even started his university studies, whatever the subject.
 
I'm not even in high school (7th grade).
 
dextercioby said:
Technically, in most axiomatizations, a state is a (unit) ray, not a vector. But this mathematical subtlety is far beyond our OP's current level of understanding, as I suspect he's not even started his university studies, whatever the subject.
Are you "nitpicking" on me? :smile:
 
Uh...
 

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