# Tag Info

### 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 ...
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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### 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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### 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 ...
• 19.8k

### 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 ...

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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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1 vote

### 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 ...
• 351k
1 vote

### 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 ...
1 vote
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### 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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