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.

4
votes
3answers
1k views

Do we or do we not observe (measure) superpositions all the time?

This is not a duplicate, the other answers do not specifically solve the contradiction, nor do they give an exact answer. I have read this question: Are we so sure about superposition? How do we ...
4
votes
2answers
249 views

Is energy $E$ in Schrödinger equation an observable/ Can $E$ be measured?

Take this quantum approach to estimate mean energy of a molecule: $$\langle\psi|H|\psi\rangle=\overline E$$ Question: Is $E$ an observable? How we can compare it to an experimental value? i.e how ...
3
votes
0answers
60 views

Do imaginary measurements exists? [duplicate]

I'm sorry if this question is too metaphysical, but I will give it a try. My textbook in introductory quantum mechanics is basing a lot of its proof and derivations on the fact that the value of the ...
2
votes
2answers
81 views

Why must momentum operator in infinite well be self adjoint?

First, let me preface this statement by saying I know that there exists no (unique) self adjoint extension of the standard differential operator for the space $L_2([0,1])$. However, when one attempts ...
6
votes
1answer
270 views

How does one actually measure the position or momentum of a quantum object?

How is the position or momentum of a Quantum particle is measured experimentally in laboratory? Suppose we want to know the position or momentum of quantum particle which is kept in a box i.e. an ...
0
votes
0answers
44 views

Eigenvalues of Unitary Matrices

I am considering the standard equation for a unitary transformation $\alpha^* = U \alpha U^{-1}$, where $\alpha$ is an arbitrary linear operator and $U$ is a unitary matrix. Since in quantum ...
0
votes
2answers
197 views

Fields: Fundamental and Physical, yet Unobservable?

I'm currently working through Robert Klauber's Student Friendly Quantum Field Theory, which by the way is much more accessible than other texts like, say, Peskin and Schroeder, for others also coming ...
4
votes
0answers
70 views

How are local observables encoded in this formulation of quantum field theory as a functor?

I've recently begun trying to understand a formulation of quantum field theory as a functor from a category of spacetimes-with-boundaries (bordisms) to a category of Hilbert spaces, as reviewed in [1]....
2
votes
1answer
70 views

What precisely must you provide to specify the Hilbert space for a particular system in quantum mechanics?

We have: $$i\hbar\frac{d |\Psi(t)\rangle}{d t} = H|\Psi(t)\rangle$$ $|\Psi\rangle$ is an element of the Hilbert space. However, the Hilbert space is unspecified. As an analogy, in classical ...
-2
votes
0answers
28 views

Proof to the Heisenberg's uncertainty principle [duplicate]

Is there a mathematical way to prove the Heisenberg's uncertainty principle? Can it be explained with the help of a probability distribution curve?
2
votes
1answer
155 views

Do observables only amount to computing functions of outcome probabilities?

It is well known that in quantum mechanics any Hermitian operator $A$ can be thought of as an observable. Given any (pure) state $\lvert\psi\rangle$, measuring such observable gives an average ...
17
votes
4answers
12k views

Why do we use Hermitian operators in QM?

Position, momentum, energy and other observables yield real-valued measurements. The Hilbert-space formalism accounts for this physical fact by associating observables with Hermitian ('self-adjoint') ...
2
votes
2answers
175 views

What does it mean for 2 observables to be compatible?

If I have 2 observable operators $A$ and $B$, if $A$ and $B$ commute: $[A, B] = 0$, then they must necessarily form a complete set of commuting observables (CSCO). Essentially, if 2 observables are ...
-2
votes
1answer
103 views

Is there a physical observable with the same units as $c/G$?

Dividing the speed of light $c$ by the gravitational constant $G$ yields the dimension mass*time/area or mass/(length * speed) Is there a physical quantity used in textbooks with this dimension? I ...
4
votes
2answers
483 views

Commutativity vs Compatibility

As far as I know, two compatible observables have a complete set of common eigenvectors, and using this fact, one can prove that their corresponding operators are commutative. Well now is the converse ...
2
votes
1answer
276 views

How to think of matrices as observables?

I'm reading Nielsen and Chuang. In one of the early chapters, they introduce some matrices such as $$X = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}.$$ They interperet this as a gate that ...
1
vote
1answer
40 views

Observing the conserved canonical momenta

Suppose I have a Lagrangian $\mathcal{L}[\phi]$ with $\phi$ a cyclic variable, which means that the Lagrangian is symmetric under shift of $\phi\rightarrow\phi+c\quad$. The equation of motion will be ...
0
votes
2answers
110 views

Is there a difference between a Hermitian operator and an observable?

My poorly written lecture notes say that any Hermitian operator does have a complete set of orthogonal eigenstates with real corresponding eigenvalues and is therefore an observable. In the article ...
3
votes
1answer
302 views

Hamiltonian symmetry Lie algebra

What is the connection between complete set of commuting observables and generators of the Lie group? I have a Hamiltonian written down in second quantized formalism and I also checked that it ...
2
votes
1answer
130 views

Simultaneous measurements in Quantum Mechanics

In the notes I am using, it states that if two observables A and B are measured simultaneously, then the measurement of A does not affect the measurement of B, and vice versa. However, why does the ...
1
vote
3answers
300 views

Is the probability current an observable?

Is the probability current in Quantum Mechanics an observable? If so, how can it me measured (directly or indirectly)?
3
votes
3answers
673 views

Why is an operator the quantum mechanical analogue of an observable?

I used to think because that, if objects are treated as waves, then using operators is the necessary thing to do in order to "retrieve" the observable from a given wavefunction. For example, in ...
10
votes
1answer
771 views

Sequential Stern-Gerlach devices - realizable experiment or teaching aid?

At least one textbook [1] uses sequential Stern-Gerlach devices to introduce to students that the components of angular momentum are incompatible observables. Viz., the $z$-up beam from a SG device ...
2
votes
1answer
317 views

Eigenvalues, Hermitian operators and observables in quantum mechanics

Consider a hermitian operator. So a) in a space of infinite dimension its eigenvectors are a base. b) in a finite-dimensional space the matrix that represents the hermitian operator is always ...
-2
votes
1answer
62 views

Quantum mechanics on operator [closed]

If any operator is commute with Hamilton then they are labelled such a way that the energy eigenstate are equal and we also know it is a constant of motion. I don't related constant of motion with ...
7
votes
6answers
1k views

Is the wave function objective or subjective?

Here is a question I am curious about. Is the wave function objective or subjective, or is such a question meaningless? Conventionally, subjectivity is as follows: if a quantity is subjective then ...
7
votes
2answers
2k views

Why hermitian, after all? [duplicate]

This question is going to look a lot like a duplicate, but I've read dozens of related posts and they don't touch the subject. Here we go. Why are observables represented by hermitian operators? ...
0
votes
2answers
174 views

Particle in a box - speed probability distribution

Consider a particle in a box with infinite barriers. By solving the Schrödinger we can find the probability of finding the particle at some points in the box. How can we find the probability of ...
1
vote
0answers
52 views

What is the variance of |S| in Bell's inequality (CHSH inequality)

Sorry that this isn't a quick question but I didn't know how to make it shorter. I am struggling with this for quite a long time and I would appreciate every help that I can get. I could not find a ...
4
votes
0answers
53 views

Measurement formalisms - POVM formalism vs Hermitian observables

I am thinking in following way of thinking about measurements in quantum mechanics. Please correct any false statements I may be making below. We start with POVMs. Let our POVM be a set of positive ...
2
votes
1answer
200 views

What exactly is the relationship between the algebraic formulation of Quantum Mechanics and the geometric formulation of Classical Mechanics?

Okay so if we consider a particular physical system, the classical description of the system starts by first introducing a symplectic manifold, which is the cotangent bundle of a configuration ...
1
vote
2answers
119 views

Meaning of time derivative of an operator

Today when my professor was deriving this equation: $$\frac{\mathrm d\langle A\rangle}{\mathrm dt}=\frac{i}{\hbar}\langle\left[H,\,A\right]\rangle+\left\langle\frac{\partial A}{\partial t}\right\...
1
vote
1answer
155 views

“Commuting observables share common eigenstates”

I am struggling to find a precise definition of this line from my quantum mechanics textbook: If $[A,B] = 0$, then the operators commute, and "commuting operators share common eigenstates". This ...
1
vote
1answer
96 views

What are the orthogonal eigenstates of the field operator?

In Peskin & Schroeder section 9.2, they derive the two-point function in the path integral formalism: $$\langle \Omega | \mathcal{T} \left\{ \hat{\phi}(x_1)\hat{\phi}(x_2)\right\} | \Omega \...
2
votes
2answers
66 views

Are $\hat x$ and $\hat p$ assumed to be time-independent operators?

In the book Quantum Mechanics by Cohen-Tannoudji, at $G_{III}$, it is given that and then in the comment section, it is also given that so I'm pretty confused in here, because in one side, they say ...
1
vote
0answers
60 views

For any two unitarily equivalent observables, can both be measured by the same experimental apparatus?

If we have an observable $A$, and a unitary operator $\hat U$, one can easily show that both $\hat A$ and $\hat U \hat A \hat U^{\dagger}$ have the same spectrum - in fact, they are called unitarily ...
1
vote
1answer
43 views

is there a way to experimentally determine the mean of $\hat A$, namely $\langle \hat A \rangle $?

Let $A$ be an observable, then, is there a way to experimentally determine the mean of $\hat A$, namely $\langle \hat A \rangle $? I mean, for example, consider the position operator; it is ...
1
vote
1answer
101 views

Is the identity operator correspond to the observable which states the existence of system?

As it is claimed in this question, the identity operator is an hermitian operator, but not an observable. However, if I were to build a device, which only measures the existence of an electron in a ...
20
votes
2answers
2k views

What Hermitian operators can be observables?

We can construct a Hermitian operator $O$ in the following general way: find a complete set of projectors $P_\lambda$ which commute, assign to each projector a unique real number $\lambda\in\mathbb R$...
20
votes
1answer
3k views

Does every hermitian operator represent a measurable quantity?

In Quantum mechanics, observables are represented by hermitian operator. But does every hermitian operator represent a observable? If not , how do we know that whether a hermitian operator represent ...
1
vote
3answers
123 views

Is there any intuitive reason behind why should the eigenfunctions of observables form a basis for our Hilbert space?

Is there any intuitive reason behind why should the eigenfunctions of observables form a basis for our Hilbert space ? For example, in the case of Stern-Gerlach experiment, sending the beam that has ...
3
votes
1answer
84 views

Is is possible to have a pair commuting observables only in a single direction?

In quantum mechanics, for two observables to be compatible, successive measurements of the observables, say $A$ and $B$, should yield the same result as earlier, i.e if we do the measurements with the ...
1
vote
0answers
164 views

Expansion of the infinite square well [closed]

I was studying the expectation value of the energy of a particle in the groud state of the infinite square well after its expansion in terms of width (from $a$ to $2a$), which is: $$\langle H\rangle= ...
0
votes
3answers
107 views

How to write an operator in matrix form?

Say I have the following operator: $$\hat { L } =\hbar { \sum_{ \sigma ,l,p } { l } \int_{ 0 }^{ \infty }\!{ \mathrm{d}{ k }_{ 0 }\,\hat { { { a }}}_{ \sigma ,l,p }^{ \dagger } } } \left({ k }_{...
1
vote
1answer
177 views

What if Schrödinger's cat's meowed?

Sorry if this has been asked (every similar question has a title that basically tags Schrödinger's cat) If after the superposition of the cat being dead and alive at one time was created, and the ...
5
votes
2answers
231 views

Question about Charge and Gauge Transformation

Does gauge invariance imply charge neutrality? I understand that all physical observables must be gauge invariant. Does this mean that physical observables must be neutral? If a quark is in red, a ...
4
votes
2answers
125 views

Significance when expectation of a commutator is zero

It is clear to me what it means when the commutator of two operator $[A, B]$ is zero and what it implies. However, is there any significance when the expectation of the commutator $\langle[A, B]\...
-1
votes
1answer
65 views

Gaussian State Spread [closed]

A measurement device which can be represented by a 1D quantum system (with canonical observables $X$ and $P$) 'is prepared in a Gaussian state with spread $s$' $$\vert \psi \rangle = \frac{1}{(\pi^2s^...
1
vote
1answer
75 views

What is 'definite' variable in QM?

I have gone through a few of the questions on the website regarding this particular query, but I have not understood what they meant. When a question says that a particle has definite momentum, are ...
1
vote
2answers
68 views

Is the period a physical observable in General Relativity?

I am currently seeing the classical tests of GR. To justify the introduction of a test based on the Doppler effect, the professor says that the previous test ( Shapiro and echo-radar test ) is based ...