# Questions tagged [observables]

A quantum observable is a measurable operator whose corresponding property of the state can be determined by some sequence of physical operations ("observation"), such as submitting the system to various electromagnetic fields and eventually reading a value. In systems governed by classical mechanics, any experimentally observable value can be shown to be given by a real-valued function on the set of all possible system states.

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### What is the physical meaning of self-adjoint operator extension?

What does it mean that there isn't any extension of a certain operator in a given domain? Does it imply that I can't apply that operator in that domain, and so that I can't measure some observables (...
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### Algebra of observables in Quantum Mechanics

When reading books about Quantum Mechanics, it is generally stated (in a kind of axiomatic way) that in Quantum Mechanics, the state of the system is represented by a vector in some Hilbert space $H$, ...
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### Variance/Standard deviation of an observable on a state that is a linear combination of eigenvectors of that observable

I know that when measuring the standard deviation of an observable the result will be zero if the system is an eigenvector of the observable on which i want to calculate the standard deviation. But ...
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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 and are the key quantities of the theory, but performing the same experiment many times would generate a distribution ...
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### Projection operator onto support of distinct observables

Suppose $P_i$ is the projection operator onto the support of the observable $O_i$ defined on some (say, finite dimensional) Hilbert space. I'm curious as to whether we can define the projection ...
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### Definition of four-velocity: why define it with proper time of the object?

The four-velocity(world-velocty) is defined by : $u^μ=\frac{dx^μ}{dτ}$ ,where $τ$ is the proper time of the object. I don't understand why it's defined with respect to the proper time but not the time ...
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### Dirac's definition of probability in quantum mechanics

I'm currently reading "The principles of quantum mechanics" by Dirac, and I'm having some trouble understanding some of his assumptions, because in the quantum mechanics course I'm following ...