# 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.

634 questions
Filter by
Sorted by
Tagged with
1 vote
50 views

### Why is this the exact shape of expectation values in the path integral formalism?

This question is about expressions of the form $$\langle x_f, t_i | \hat{x}(t) | x_i, t_i \rangle = \frac{1}{N} \int_{x(t_i) = x_i}^{x(t_f) = x_f} \mathcal{D} x~x(t)e^{i S[x]}.$$ In the following ...
132 views
+100

57 views

### Unmeasurable observables in quantum mechanics

Let's consider a single particle in 1D harmonic oscillator for definiteness. In standard QM, we say that any Hermitian operator on the Hilbert space is an "observable". It seems that (in ...
116 views

### What does it mean to "quantise" a system?

Suppose we have a physical system, let's say a ring of $N$ atoms held together by elastic force. (This is just an example, we could have picked any physical system) Classically we can easily find the ...
70 views

### What are measurable physical quantities?

The book "Fundamentals of many body physics" by Wolfgang Nolting at the beginning of chapter 3 says: Measurable physical quantities are: the eigenvalues of observables the expectation ...
1 vote
51 views

### Intuition for momentum operator in position space

The derivation of the momentum operator in position space. But, several assumptions are usually made that a) we are dealing with the particle in free space or b) that the two representations are ...
93 views

### Valid Intuition? - Why observables are represented by eigenstates/eigenvalues

So I've been frustrated with the usual presentation of the operator formalism being presented as an axiom, and have been after a more intuitive explanation. Would the following intuition be considered ...
24 views

1 vote
103 views

### Repeating observations in quantum theory

Suppose we prepare a state $\psi$ in a quantum system, represented in some Hilbert space, and suppose $A$ is an observable represented by the matrix $A$ (which possibly has infinite order). QUESTION A ...
1 vote
111 views

### Is the uncertainity principle explained by disturbances or only by the Fourier picture?

Qualitatively, the tradeoff in uncertainty between two non-commuting observables $\hat{x}$ and $\hat{y}$, could be explained by... the Fourier picture where the more one variable is defined (i.e., ...
89 views

76 views

### How to simply explain 'quantum state' to a beginner?

While explaining 'quantum state' to a beginner, is it scientifically accurate to say that "just like '$v$' represents velocity and '$p$' represents the momentum of an object, $|ψ\rangle$ ...
57 views

### What is the fundamental observable in casual set theory?

In ordinary quantum theory or string theory, the fundamental observables are correlation functions or scattering amplitude that can be measured by particle physics experiments . In loop quantum ...
71 views

### Trying to understand post-measurement density matrices in a state that spans 2 Hilbert spaces

What I would like to understand mathematically is the following situation: Prepare a quantum state that spans two Hilbert spaces Operate on one space with observable operator $\hat{O}$. Obtain ...
35 views

### Can an Hermitian unitary matrix in a Hilbert-rigged space be 3-dimensional?

While studying a couple of concepts, I've understood the following premises to be true: Hermitian unitary matrices eigenvalues are unimodal (that's $\pm1$). In physics, operators/observables are ...
75 views