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2
votes
1answer
49 views

Which of the properties of particles are intrinsic properties and why?

For macroscopic objects it's clear that - once observed - the observed property does exist for a while, even if we are no longer observing it. That has to do with the complexity and stability of such ...
2
votes
4answers
143 views

Is what statisticians call a “random variable” what physicists call an “observable” in QM? [duplicate]

I read at http://www.statlect.com/fundamentals-of-probability/random-variables that A random variable is a variable whose value depends on the outcome of a probabilistic experiment. Its value is ...
2
votes
1answer
65 views

Conservation of momentum in infinite square well

This is inspired by Griffiths QM section 2.2, on the infinite square well, which is about how far I've gotten (so, sorry if this is addressed later in the book). For any given starting wavefunction, ...
2
votes
2answers
50 views

Why do $\hat{X}$ and $\hat{P}$ have to correspond to position and momentum?

As far as I understand, in QM we treat observables as operators, and the eigenvalues of these operators are the possible values we can measure of the observables. It is usually simpler to work in the ...
3
votes
0answers
48 views

Simultaneous measurement of non-commuting observables without uncertainty

A pair of non-commuting Observables $\hat{X}$ and $\hat{P}$ does not have a common set of eigenfunctions, i.e., it can not be measured simultaneously. Let us for the sake of simplicity assume that ...
1
vote
0answers
29 views

Volume Operator / volume phase-space-function in thermodynamics

In Thermodynamics, one often encounters the derivation of pressure as the generalised force that belongs to the extensive state-variable of the volume. Postulates: One looks just at a system of many ...
3
votes
2answers
109 views

Interpretation of $\langle \phi | A | \psi \rangle$ [duplicate]

If the current state of some quantum system is $| \psi \rangle$, what is the physical interpretation of $$ \langle \phi | A | \psi \rangle $$ where $|\phi\rangle$ is some other -maybe the same- ...
4
votes
0answers
62 views

Measuring the Dirac field

If the Dirac field $\psi(x)$ is to the electron as the Electromagnetic field is to the photon, why is it that we can measure the Electromagnetic field, whereas the Dirac field we cannot?
1
vote
0answers
43 views

Measuring expectation value in quantum field theory and in quantum mechanics

There is a way of calculating the vacuum expectation value $\langle 0|\hat\phi|0\rangle$ theoretically in a quantum field theory like there is a rule to compute expectation value of any operator A ...
0
votes
0answers
24 views

What are physical observables that are connected to orbital angular momentum?

We considered a system that is confined to a curved surface. In the quantization process, we have obtained an additional orbital angular momentum that are from the surface geometrical deformation. Now ...
5
votes
2answers
161 views

Is there a time operator in quantum mechanics?

The question in the title has been asked many times on this site before, of course. Here's what I found: Time as a Hermitian operator in QM? in 2011. Answer states time is a parameter. Is there an ...
1
vote
0answers
59 views

How to measure $\mathbb{L}^2$ and $L_z $ simultaneously

What does an experiment look like, in which both quantities are measured simultanously?
0
votes
1answer
70 views

Is the collapsed wavefunction a solution of Time-dependent Schrodinger equation?

For measurement of any observable associated with the particle, should the wavefunction after collapse be a solution of the time-dependent Schrodinger equation? A general solution of the time ...
1
vote
2answers
43 views

Measurement of position after collapse of a wavefunction

Suppose I have a wavefunction which collapses to a certain eigenstate after a measurement of energy. In that state, I perform a calculation of position and obtain a certain position value, say $x_0$. ...
0
votes
1answer
56 views

Relativistic Commutation relation for momentum and position

We all know that the canonical commutation relation give you $$[x_i,p_j]=i\hbar\delta_ij,$$ is there a relativistic version such as $$[x^a,p_b]=i\hbar\delta_a^b?$$ If so what is the time ...
3
votes
0answers
77 views

Is there a physical significance to non-normal states of the algebra of observables?

Quantum theory may be formalized in several different ways. Generally, the physical discussion of different states of a quantum system distinguishes pure and mixed states, and then subsumes both in a ...
1
vote
0answers
52 views

Why Hamiltonian is Hermitian? [duplicate]

Everyone knows that this is needed to make eigenvalues real, but still why we enforcing such a structure at first place? An arbitrary operator can have as complex as real eigenvalues, we can simply ...
0
votes
1answer
42 views

Distinguishing degenerate states physically

Suppose there is a free particle on a circle with radius r. The energy spectrum is then $$E_n = \frac{n^2\hbar^2}{2mr^2} \,.$$ Thus, when $n \neq 0$, then the spectrum of energies is degenerate ...
0
votes
2answers
100 views

Physical quantities have definite values?

I don't really know if this question has an anwser but I thought it was worth to try asking. My point here is the following: in Quantum Mechanics, to describe the states of a system we use a Hilbert ...
2
votes
0answers
81 views

Is there any additional complexity in the physical laws that seems unnecessary for us to exist? [closed]

I am wondering if the universe is as simple as possible, at least given the constraint that humans exist on Earth. This is my second attempt at this question, which was marked as too broad, since I ...
2
votes
0answers
41 views

Have Witten-type TQFT's nonconservation of energy and momentum in interactions?

Witten-type topological quantum field theories are based on cohomology theories. Every observable must lie in a cohomology class. May be $G$ a geometric field. Then every observable expectation value ...
4
votes
2answers
272 views

Why don't non-Hermitian operators with all real-eigenvalues correspond to observables? [duplicate]

Suppose you could construct an operator that was non-Hermitian but had all real eigenvalues or could at least be restricted in a way to create only real eigenvalues, why would this operator not ...
4
votes
4answers
158 views

How to determine the observables rigorously?

In Quantum Mechanics, as I know, if a system is described by a Hilbert space $\mathcal{H}$, each physical quantity is associated with some hermitian operator $A : U\subset \mathcal{H}\to \mathcal{H}$ ...
1
vote
1answer
73 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 ...
1
vote
3answers
75 views

Is the perturbation Hamiltonian an observable?

In fine structure calculation we use the perturbation theory. The basic Hamiltonian $H_0$ is perturbed as: $H = H_0 + W$ First, the basic problem assume that $H_0$ is an observable. That allows to ...
0
votes
1answer
96 views

spin independent observable [closed]

Let's consider a spin independent observable $O$ (the terms of the operator don't depend upon the spin operator). If we are interested to find an eigenfunctions' basis of the wave-functions' space, ...
0
votes
2answers
118 views

Function of observables in mathematical words

In mathematical words, an observable is an operator that a set of linearly independent eigenfunctions constitutes a complete basis of the wave-functions' space. Now, let's consider some observables: ...
0
votes
3answers
117 views

Both Eigenvalues and Operators are “Observables”? [duplicate]

I am having a bit of difficulty wading through the what seems to be multiple usages for Observables in Quantum Mechanics. " Mathematically observables are postulated to be Hermitian operators.. " ...
2
votes
1answer
150 views

Why isn't the time-derivative considered an operator in quantum mechanics? [duplicate]

Based on my understanding when doing quantum mechanics we deal with a small set of mathematical objects: namely scalars, kets, bras, and operators. But then in the Schrodinger equation we have this ...
6
votes
2answers
132 views

What does it mean to observe? [duplicate]

This is a layman's question. The only thing I know about quantum physics is from casual reading and documentaries. I can imagine electrons being probabilistic waves. Their position is an infinite ...
0
votes
1answer
43 views

Lorentz Symmetry

Quick question about Lorentz symmetry. From the wiki page the feature of nature that says experimental results are independent of the orientation or the boost velocity of the laboratory through ...
3
votes
1answer
357 views

The dual role of (anti-)Hermitian operators in quantum mechanics

Hermitian (or anti-Hermitian) operators are of central importance in quantum mechanics in at least two different incarnations: Observables are represented by Hermitian operators on the quantum ...
1
vote
1answer
41 views

“Independent simultaneous eigenbras” in Dirac's book 'Principles of Quantum Mechanics'

I've been puzzling through this book off and on and can usually work out what is going on via other external references on the Intertubes. But, this paragraph from pages 55 and 56 has me a bit ...
1
vote
3answers
244 views

Why is only one quantity of angular momentum i.e. $L_z$ quantized & not $L_x$ & $L_y$?

This is quoted from Arthur Beiser's Concepts of Modern Physics: Why is only one quantity of $\mathbf{L}$ quantized? The answer is related to the fact that $\mathbf{L}$ can never point in any ...
0
votes
3answers
87 views

Do we get the same answer at any time if we measure a system's energy?

Schrödinger's equation says that the only allowed energy states of a system are the eigenvalues of the energy operator $H$. This means that if we measure the energy of the system at any time we ...
13
votes
4answers
1k views

Really how can an observable quantity be equal to an operator?

A wave-function can be written as $$\Psi = Ae^{-i(Et - px)/\hbar}$$ where $E$ & $p$ are the energy & momentum of the particle. Now, differentiating $\Psi$ w.r.t. $x$ and $t$ respectively, ...
0
votes
1answer
58 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 ...
0
votes
2answers
108 views

Would $[\hat{Q},\hat{H}]$ correspond to an observable? [closed]

Would $[\hat{Q},\hat{H}]$ correspond to an observable? Where $\hat{Q}$ is an observable and $\hat{H}$ is the Hamiltonian. Surely that would just mean that $[\hat{Q},\hat{H}]$ would commute i.e. = 0?: ...
-1
votes
1answer
541 views

How to derive Uncertainty Principle relation?

How to derive Heisenberg Uncertainty Principle relation?
0
votes
1answer
77 views

How might I show that an operator is, by definition, an 'observable'? [closed]

Here is my problem: I understand what is meant by 'observable' but don't have a formal definition at hand. How do I 'show' it?
1
vote
1answer
67 views

Compatible Observables and Measurement

Suppose $A$ and $B$ are compatible observables (i.e. $[A,B] = 0$). We take the eigenkets of $A$ to be $|a_1 \rangle \ldots |a_N \rangle$. Further, we suppose that the first $k$ eignekets of $A$ are ...
3
votes
2answers
236 views

What exactly implies the need of quantum mechanics for self-adjoint and not only symmetric operators? [duplicate]

We know that quantum mechanics requires self-adjoint operators, not only symmetric. Can we say that this follows ONLY from the two following axioms of quantum mechanics, namely that each observable ...
1
vote
3answers
217 views

What is the meaning of “ Ψ is not a measurable quantity in itself”?

I want to know that why the wavefunction Ψ as a complex quantity (i.e $A+iB$ form) in quantum mechanics and somewhere I have studied that Ψ is not a measurable quantity in itself that's why we ...
0
votes
1answer
79 views

Quantum state of a system after measurements with non-commutative operators

a) Assume two operators $A$ and $B$. 1) Assume $$[A,B]=0 $$ and $$ ψ= \sum c_n u_n ~~~~\text a~ wavefunction~ describing~ the~ state~ of~ the~ system $$ with $$Aψ=a_n u_n $$ $$Bψ=b_n u_n$$ If we ...
2
votes
1answer
150 views

About states, observables and the wave functional interpretation in QFT with gauge fields

First of all, I'm a mathematician, so forgive me for my possible trivial mistakes and poor knowledge of physics. In a QFT, we just start with a field (scalar, vectorial, spinorial, gauge etc), so I ...
1
vote
3answers
250 views

Constants of motion in quantum mechanics

What is the meaning of a constant of motion in quantum mechanics (an observable-operator that commutes with the Hamiltonian) in contrary with classical mechanics?
5
votes
1answer
397 views

Is color charge a quantum mechanical observable?

If I had 2 pions that were identical, except one was comprised of a red and anti-red, and the other was comprised of a green and anti-green, would I be able to perform an experiment that distinguishes ...
-4
votes
2answers
146 views

Classical notion of trajectory [closed]

Why the classical notion of trajectory is meaningless in quantum mechanics? I am asking here about notion of trajectory from classical mechanics and why in quantum mechanics we cannot use it or is ...
2
votes
2answers
525 views

Susceptibilities and response functions

It is often confusing whether a susceptibility is the same as a response function, specially that often they are used interchangeably, in the context of statistical mechanics and thermodynamics. Very ...
2
votes
1answer
270 views

Singlet state and it's expectation value

So. We have a singlet sate $$ \dfrac{1}{\sqrt{2}}(\vert\uparrow\downarrow\rangle-\vert\downarrow\uparrow\rangle)$$ And two pauli matrices for z axis - one that acts on 1st spin (lets denote it with ...