The observables tag has no wiki summary.
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Can we measure “wavefunction” of quantum particles?
We know that there is uncertainty principle, so question: can we ever measure wavefunction of particles? I do not think this is possible, but I am not sure. I guess that everything is probabilistic. ...
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3answers
207 views
Is every quantum measurement reducible to measurements of position and time?
I am currently studying Path Integrals and was unable to resolve the following problem. In the famous book Quantum Mechanics and Path Integrals, written by Feynman and Hibbs, it says (at the beginning ...
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465 views
In what sense is a scalar field observable in QFT?
Consider a QFT consisting of a single, hermitian scalar field $\Phi$ on spacetime (say $\mathbb R^{3,1}$ for simplicity). At each point $x$ in spacetime, $\Phi(x)$ is an observable in the sense that ...
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“An operator is hermitian”. Implications?
Alastair Rae states that there are 4 postulates of Quantum Mechanics in his text on the subject matter. The first part of his second postulate can be stated as:
Every dynamical variable may be ...
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2answers
128 views
What does the quantum state of a system tell us about itself?
In quantum mechanics, quantum state refers to the state of a quantum
system. A quantum state is given as a vector in a vector space, called
the state vector. The state vector theoretically ...
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1answer
372 views
Intuitive meaning of Hilbert Space formalism
I am totally confused about the Hilbert Space formalism of Quantum Mechanics. Can somebody please elaborate on the following points:
The observables are given by self-adjoint operators on the ...
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2answers
225 views
Eigenvalues of a quantum field?
Fields in classical mechanics are observables. For example, I can measure the value of the electric field at some (x,t).
In quantum field theory, the classical field is promoted to an operator-valued ...
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2answers
194 views
Does every measurement correspond to an eigenstate of an observable?
In the postulates of quantum mechanics, physical observables are described by Hermitian matrices on the state space of a system.
In another of my questions, the measurements of Rydberg-Ritz spectral ...
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3answers
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What determines which observables are QM?
Spin, position, and velocity are observables which are QM for quantum particles. My question is, what determines whether an observable is QM or not?
For example, why is electric charge not QM? That ...
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1answer
167 views
proof for $\langle q| p \rangle = e^{ipq}$
What would be the proof for $\langle q| p \rangle = e^{ipq}$?
Is it derived from canonical commutation relation?
($|q \rangle $ represents the position eigenstate, while $|p \rangle$ represents the ...
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3answers
317 views
Why is $\int (dp/2\pi) |p \rangle\langle p| = 1 $?
In quantum mechanics, why is $\int (dp/2\pi) |p \rangle\langle p| = 1 $ where $|p \rangle$ represents momentum eigenstate?
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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') ...
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Hamiltonian of oscillators quantized proof
https://docs.google.com/open?id=0BxrBcN1-BZWUOXNxR1l4S0l2MjQ
http://www.2shared.com/complete/Qjy1_uzp/Quantum_Mechanics_in_Simple_Ma.html
(I uploaded a pdf file that contains the parts of the ...
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3answers
1k views
Proof of Canonical Commutation Relation (CCR)
I am not sure how $QP-PQ =i\hbar$ where $P$ represent momentum and $Q$ represent position. $Q$ and $P$ are matrices. The question would be, how can $Q$ and $P$ be formulated as a matrix? Also, what is ...
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2answers
161 views
Why does $i ( LK-KL )$ represent a real quantity?
According to my textbook, it says that $i( LK-KL )$ represents a real quantity when $K$ and $L$ represent a real quantity. $K$ and $L$ are matrices. It says that this is because of basic rules. ...
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Direction vector of a physical quantity matrix
A physical quantity can be represented by the following form:
$A = a_1\sigma_1 + a_2\sigma_2 + a_3\sigma_3$ where $\sigma$ matrices are Pauli matrices.
Also suppose that there is $B = b_1\Sigma_1 + ...
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How to express continuous values as a matrix
Usually a quantity of a matrix is defined as the eigenvalues of the matrix. If so, how can anyone express continuous values, as in Schrodinger picture, into a matrix?
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If $L$ is a matrix that represents real physical quantity, why is $L^2$ non-negative real physical quantity?
In my textbook, it says that when $L$ is a matrix that represents real($\mathbb{R}$) physical quantity, $L^2$ represents non-negative real physical quantity. What would be the proof of this?
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1answer
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Commutability of two physical quantity matrices
Suppose that two matrices $A$ and $B$, representing real($\mathbb{R}$) physical quantity, can be multiplied commutatively with each other; i.e. $AB =BA$. However, each matrix cannot be multiplied ...
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Is the expectation value always an eigenvalue?
Does the expectation value of an observable must be equal to an eigenvalue of the corresponding operator?
I already know that 0 is not an eigenvalue, but is there any other examples?
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4answers
258 views
Complete set of observables in classical mechanics
I'm reading "Symplectic geometry and geometric quantization" by Matthias Blau and he introduces a complete set of observables for the classical case:
The functions $q^k$ and $p_l$ form a complete ...
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2answers
225 views
Symmetries, Generators, Commutators and Observables
I'm learning about generators and conservation laws and have derived the equation (1)
$$[Q,A]=-i\hbar f(A)$$
which is satisfied by the observable generator $Q$ for a transformation group with ...
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1answer
152 views
Does spontanous symmetry breaking affect Noethers theorem?
Does spontanous symmetry breaking affect the existence of a conserved charge?
And how does depend on whether we look at a classical or a quantum field theory (e.g. the weak interacting theory)?
...
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Books on the general notions of measurements, observables, states, etc.? [closed]
I am reading the intro chapter in Huzihiro Araki's Mathematical Theory of Quantum Fields, which discusses the general notions of states, measurements, and observables (e.g. the topology on the sets of ...
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Are the only observables in string theory the S-matrix?
Is the S-matrix the only observable in string theory? What about time varying spacetime backgrounds, or thermal states then?
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397 views
Why does spin have a discrete spectrum?
Why is it that unlike other quantum properties such as momentum and velocity, which usually are given through (probabilistic) continuous values, spin has a (probabilistic) discrete spectrum?
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1answer
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Conserved quantum observables from symmetries *with density matrix*
I’ve read Ballentine where he derives the conserved observable operators (momentum, energy, ...) from symmetries of space-time.
Can I read up such a derivation in more detail somewhere else or even ...
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1answer
129 views
The difference between projection operators and field operators in QFT?
Is there a good reference for the distinction between projection operators in QFT, with an eigenvalue spectrum of $\{1,0\}$, representing yes/no measurements, the prototype of which is the Vacuum ...
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3answers
32 views
Constructing a CP map with some decaying property
Given some observable $\mathcal O \in \mathcal H$ it is simple to construct a CP (completely positive) map $\Phi:\mathcal{H}\mapsto \mathcal{H}$ that conserves this quantity. All one has to observe is ...
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313 views
Some questions on observables in QM
1-In QM every observable is described mathematically by a linear Hermitian operator. Does that mean every Hermitian linear operator can represent an observable?
2-What are the criteria to say whether ...
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1answer
859 views
Compatible Observables
My QM book says that when two observables are compatible, then the order in which we carry out measurements is irrelevant.
When you carry out a measurement corresponding to an operator $A$, the ...
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What exactly is the 'observer' in physics and/or quantum mechanics? [duplicate]
Possible Duplicate:
nature of an observer
For instance, in the double slit experiment, what is exactly defined as an observer?
I remember from somewhere, light is also an observer?
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1answer
455 views
“Completeness” of eigenvectors in a complete, commuting set
This question was originally the one below dashed line. Now after further discussions, it has boiled down to this question:
Is the following construction possible? Suppose we have a 3 dimensional ket ...
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2answers
130 views
Uniqueness of eigenvector representation in a complete set of compatible observables [duplicate]
Possible Duplicate:
Uniqueness of eigenvector representation in a complete set of compatible observables
Sakurai states that if we have a complete, maximal set of compatible observables, ...
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2answers
300 views
Uniqueness of eigenvector representation in a complete set of compatible observables
Sakurai states that if we have a complete, maximal set of compatible observables, say $A,B,C...$ Then, an eigenvector represented by $|a,b,c....>$, where $a,b,c...$ are respective eigenvalues, is ...
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Observables with transcendental eigenvalues
Are there any "natural" physical observables which have non-empty point spectrum which consists of numbers which are not algebraic numbers?
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How does non-commutativity lead to uncertainty?
I read that the non-commutativity of the quantum operators leads to the uncertainty principle.
What I don't understand is how both things hang together. Is it that when you measure one thing first ...
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3answers
398 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 ...
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What is an observer in quantum mechanics?
My question is not about (pseudo) philosophical debate; it concerns mathematical operations and experimental facts.
What is an observer? What are the conditions required to be qualified of observer, ...
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319 views
Is it possible to define a “it went through two slits” observable?
This concerns the famous two-slit experiment. Electrons or photons or your favorite particle, doesn't matter. As we all know, the attempt to detect which slit the quanta pass through leads to loss ...
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Diff(M) and requirements on GR observables
This question is kind of inspired in this one:
Diff(M) as a gauge group and local observables in theories with gravity
The conundrum i'm trying to understand is how is derived the (quite) ...
