# Tagged Questions

The observables tag has no wiki summary.

2answers
99 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 ...
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 ...
2answers
459 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 ...
1answer
167 views

### “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 ...
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 ...
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 ...
2answers
127 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 ...
2answers
129 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, ...
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 ...
1answer
370 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 ...
2answers
223 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 ...
2answers
192 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 ...
3answers
178 views

### 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 ...
3answers
316 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?
1answer
166 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 ...
2answers
139 views

### 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?
3answers
556 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') ...
2answers
344 views

### 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 ...
3answers
988 views

### 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 ...
2answers
160 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. ...
3answers
144 views

### 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?
0answers
93 views

### 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 + ...
1answer
156 views

### 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 ...
2answers
396 views

### 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?
4answers
257 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 ...
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 ...
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)? ...
0answers
45 views

### 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 ...
2answers
136 views

### 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?
3answers
393 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?
6answers
610 views

### 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, ...
10answers
525 views

### 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?
3answers
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 ...
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 ...
1answer
195 views

### 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 ...
1answer
851 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 ...
2answers
239 views

### 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?
3answers
317 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 ...
2answers
289 views

### 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) ...
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 45, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.9012514352798462, "perplexity_flag": "middle"}