The probability when the wave-function collapses

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Discussion Overview

The discussion revolves around the concepts of wave-function collapse, the projection postulate, and the Born rule in quantum mechanics. Participants explore the relationship between these concepts, particularly in the context of measurement and probability distributions.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation
  • Homework-related

Main Points Raised

  • Some participants assert that the projection postulate describes wave-function collapse to eigenstates, while questioning how probabilities for these outcomes are determined.
  • Others clarify that the probabilities associated with measurement outcomes are defined by the Born rule, distinguishing it from the projection postulate.
  • A participant challenges the idea that the Born rule and Born's ##\psi## interpretation are the same, suggesting that they serve different purposes in quantum mechanics.
  • Another participant argues that there is no probability distribution independent of measurements in quantum mechanics, asserting that the probability density ##|\psi(x)|^2## is a direct application of the Born rule.
  • There is a request for examples or exercises that utilize the projection postulate and the Born rule, indicating a desire for practical applications of these concepts.
  • Participants suggest looking into quantum mechanics textbooks for exercises related to the discussed concepts.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between the Born rule and Born's ##\psi## interpretation, with no consensus reached on whether they are the same or distinct concepts. The discussion remains unresolved regarding the clarity of the initial question posed by one participant.

Contextual Notes

Some statements reflect assumptions about the definitions and relationships between quantum mechanics concepts, which may not be universally accepted. The discussion also includes references to specific textbooks and articles for further exploration of the topics.

Who May Find This Useful

Readers interested in quantum mechanics, particularly those exploring the foundational concepts of wave-function collapse, measurement, and probability in quantum theory.

thaiqi
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TL;DR
The projection postulate
Hello, everyone. The projection postulate says the wave-function collapses to one of its eigenstates under measurement, does it talk about each probability with which the wave-function collapses to those possible eigenstates?
 
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No, the probabilities for the different measurement outcomes are part of a another postulate which is called the Born rule.
 
kith said:
No, the probabilities for the different measurement outcomes are part of a another postulate which is called the Born rule.
Thanks. So the Born rule and Born's ##\psi## interpretation are two different things?(Sorry I can't visit wiki )
 
No, they are the same (or at least closely related).
 
kith said:
No, they are the same (or at least closely related).
Why do you say they are the same? Born rule is for measurement, while the Born's ##\psi## interpretation is for the probability distribution in the space of particles(which has nothing to do with measurement). Shouldn't they have nothing to do with each other?
 
thaiqi said:
Born rule is for measurement, while the Born's ##\psi## interpretation is for the probability distribution in the space of particles(which has nothing to do with measurement).
That's not correct. There isn't a probability distribution independent of measurements in QM. ##|\psi(x)|^2## being a probability density is just the Born rule in the special case of position being measured.

What is this thread about?
 
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kith said:
What is this thread about?
Sorry I don't understand this question.
 
thaiqi said:
Sorry I don't understand this question.

His question means that we don't understand what your issue is.
 
PeterDonis said:
His question means that we don't understand what your issue is.
Are there any exercises examples that use this projection postulate and need to use Born rule when computing?
 
Last edited:
  • #10
thaiqi said:
Are there any exercises examples that use this projection postulate and need to use Born rule when computing?

Have you tried looking in textbooks on QM? They have lots of exercises.
 
  • #11
PeterDonis said:
Have you tried looking in textbooks on QM? They have lots of exercises.

Thanks. I found two: Laloe's and Norsen's.
The other two maybe of help: Neumaier's and Nelson Bolivar's.
Also, Matteo Paris's article maybe is of help (The modern tools of quantum mechanics).
 
  • #12
thaiqi said:
I found two

Good, then go do the exercises in them. If you have questions about a particular exercise, you can start a new thread (in the homework forum, since that's where questions about textbook exercises should go).

This thread is closed.
 

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