17
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Why are expectation values of an observable important in QM?
This is an important point which should be discussed.
What one obtains from experiments are frequencies of outcomes of given measured observables on an ensemble of identical quantum systems all ...
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9
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Accepted
Dirac's definition of probability in quantum mechanics
I'm currently reading "The principles of quantum mechanics" by Dirac...
...What I don't get is the following part, where he writes:
In the general case we cannot speak of an observable ...
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6
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Why are expectation values of an observable important in QM?
As an add-on to the fantastic answer of Valter Moretti I would like to say that people are in the business of working out full probability distributions for measurements (usually by the name "...
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6
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Why are expectation values of an observable important in QM?
The reason that people care about expectation values -- that is, the average result observed in an experiment -- is to some extent historical. In early quantum mechanical experiments, one would ...
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5
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Dirac's definition of probability in quantum mechanics
Once one identifies $\langle x | A |x \rangle $ with the average value of $A$, and the states $|x\rangle$ are normalized, it is just the frequentist definition of probability that forces to identify ...
4
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Dirac's definition of probability in quantum mechanics
This has nothing to do with quantum mechanics. Imagine you're tossing a fair die. You can assign any numbers to the six outcomes. If you number them $1,2,3,4,5,6$ then the expected value of a roll is $...
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3
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Why are expectation values of an observable important in QM?
This situations is not specific to Quantum Mechanics and the reason is quite simple. Basically, whenever you need to deal with a random event experimentally (we sometimes forget that Physics is not ...
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2
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Why are expectation values of an observable important in QM?
I've been reading that expectation values of an observable is all what we can get
What you have been reading is oversimplified. By making multiple measurements on a system in an identical state (or a ...
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2
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Can you pre-determine the result of a coin toss?
The answer to the question is a simple “yes”. This has been investigated a few times in the 20th century, but in 2007 Diaconis, Holmes and Montgomery even built a machine that executes exactly the ...
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Most probable position of finding an electron represented in cartesian and spherical coordinates
I believe that more cautions notation and terminology would make this less confusing.
The probability of a measurement in a cuboid-shaped volume bounded by $x\in(x',x'+\delta x)$, $y\in(y',y'+\delta y)...
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What is a cross section, really?
Cross sections are quoted in area (usually barn with some prefix), which is like a measure of how small of a target you have to hit. The matrix element gives a probability of a scattering event, that ...
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Why are expectation values of an observable important in QM?
Suppose we are measuring some property $A$ of a quantum system, and the system is in a superposition of states with different values of $A$:
$$ \Psi = \sum c_i \phi_{Ai} $$
Before we do the ...
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1
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Why are expectation values of an observable important in QM?
The reason behind physicists focusing solely on the Expectation values of an observable lies in the probabilistic nature of Quantum mechanics. If our experiment remains unbiased, repeatedly performing ...
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1
vote
Accepted
Boundary Pressure of a system in the Grand Canonical Ensamble
I agree that Kerson Huang's textbook sometimes has sloppy derivations. In this case, however, the book complicates a quite simple derivation.
Indeed, his formula for the variance of the number ...
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