Operators Definition and 1000 Threads

This is a list of operators in the C and C++ programming languages. All the operators listed exist in C++; the fourth column "Included in C", states whether an operator is also present in C. Note that C does not support operator overloading.
When not overloaded, for the operators &&, ||, and , (the comma operator), there is a sequence point after the evaluation of the first operand.
C++ also contains the type conversion operators const_cast, static_cast, dynamic_cast, and reinterpret_cast. The formatting of these operators means that their precedence level is unimportant.
Most of the operators available in C and C++ are also available in other C-family languages such as C#, D, Java, Perl, and PHP with the same precedence, associativity, and semantics.

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  1. C

    General commutation relations for quantum operators

    (This is not a homework problem). I'm an undergrad physics student taking my second course in quantum. My question is about operator methods. Most of the proofs for different commutation relations for qm operators involve referring to specific forms of the operators given some basis. For...
  2. B

    Other Understanding Physics Operators: A Comprehensive Guide

    Where can I find a PDF or book that explains what are and how to use the operators?
  3. Jianphys17

    I The role of the weight function for adjoint DO

    Hi at all, I've a curiosity about the role that the weight function w(t) she has, into the define of adjoint & s-adjoint op. It is relevant in physical applications or not ?
  4. D

    I Vector Operators in Quantum Mechanics: Adapting to Different Coordinate Systems

    I have always seen “vector” operators, such as the position operator ##\vec R##, defined as a triplet of three “coordinate” operators; e.g. ##\vec R = (X, Y, Z)##. Each of the latter being a bona fide operator, i.e. a self-adjoint linear mapping on the Hilbert space of states ##\mathcal H##. (I...
  5. F

    Insights Why do we need Hermitian generators for observables in quantum mechanics?

    fresh_42 submitted a new PF Insights post How to Tell Operations, Operators, Functionals and Representations Apart Continue reading the Original PF Insights Post.
  6. Jianphys17

    I Fredholm integral equation with separable kernel

    Hi at all On my math methods book, i came across the following Fredholm integ eq with separable ker: 1) φ(x)-4∫sin^2xφ(t)dt = 2x-pi With integral ends(0,pi/2) I do not know how to proceed, for the solution...
  7. Wrichik Basu

    B QFT for Beginners: Operators & Their Physical Significance

    I'm a beginner in QFT, starting out with D. J. Griffiths' book in this topic. I have a question on the operators used in QM. What are operators? What is the physical significance of operators? I can understand that ##\frac {d}{dt}## to be an operator, but how can there be a total energy...
  8. Danny Boy

    A Forming a unitary operator from measurement operators

    If we consider a measurement of a two level quantum system made by using a probe system followed then by a von Neumann measurement on the probe, how could we determine the unitary operator that must be applied to this system (and probe) to accomplish the given measurement operators.
  9. D

    I Kinetic and Potential energy operators commutation

    Hi All, Perhaps I am missing something. Schrodinger equation is HPsi=EPsi, where H is hamiltonian = sum of kinetic energy operator and potential energy operator. Kinetic energy operator does not commute with potential energy operator, then how come they share the same wave function Psi? The...
  10. Jamison Lahman

    I Exploring Logical Operators in Electronic Circuits: A Refreshing Reminder

    While at university, we went over logical operators for our electronic circuits lab. There was one that depended on the previous value which fascinated my deeply, but for some reason I can't remember it. I only vaguely remember it so I apologize if I mess up what actually happened. From what I...
  11. binbagsss

    Strings, Virasoro Operators & constraints, mass of state

    Homework Statement Question: (With the following definitions here: - Consider ##L_0|x>=0## to show that ##m^2=\frac{1}{\alpha'}## - Consider ##L_1|x>=0 ## to conclude that ## 1+A-2B=0##- where ##d## is the dimension of the space ##d=\eta^{uv}\eta_{uv}## For the L1 operator I am able to get...
  12. binbagsss

    Strings, Virasoro Operators&constraints, commutator algrebra

    Homework Statement [/B] Question: (With the following definitions here: ) - Consider ##L_0|x>=0## to show that ##m^2=\frac{1}{\alpha'}## - Consider ##L_1|x>=0 ## to conclude that ## 1+A-2B=0## - where ##d## is the dimension of the space ##d=\eta^{uv}\eta_{uv}## For the L1 operator I am...
  13. S

    A Operators in Quantum Mechanics

    Hey guys, Am facing an issue, we know that x and y operators take the same form due to isotropy of space, but sir if we destroy the isotropy, then what form will it take? Can u pleases throw some light on this! Thanks in advance
  14. binbagsss

    Strings - Visaro operators - basically commutator algebra

    Homework Statement Question: (With the following definitions here: ) - Consider ##L_0|x>=0## to show that ##m^2=\frac{1}{\alpha'}## - Consider ##L_1|x>=0 ## to conclude that ## 1+A-2B=0## - Consider ##L_2|x>=0 ## to conclude that ##d-4A-2B=0## - where ##d## is the dimension of the space...
  15. B

    I Angular momentum operator commutation relation

    I am reading a proof of why \left[ \hat{L}_x, \hat{L}_y \right ] = i \hbar \hat{L}_z Given a wavefunction \psi, \hat{L}_x, \hat{L}_y \psi = \left( -i\hbar \right)^2 \left( y \frac{\partial}{\partial z} - z \frac {\partial}{\partial y} \right ) \left (z \frac{\partial \psi}{\partial x} -...
  16. D

    Where did I miss a minus sign?

    Homework Statement Homework EquationsThe Attempt at a Solution 1.1st circle on the left : where did I miss a minus sign? 2. How to show that the last term is equal to 1? Thanks!
  17. D

    I Products of operators : products of matrices

    Hi. If I have an operator in matrix form eg. < i | x | j > then the matrix of the operator x2 is given by the square of the former matrix. This seems like common sense but how would i prove this using Dirac notation ? Thanks
  18. binbagsss

    Complex scalar field -- Quantum Field Theory -- Ladder operators

    Homework Statement STATEMENT ##\hat{H}=\int \frac{d^3k}{(2\pi)^2}w_k(\hat{a^+(k)}\hat{a(k)} + \hat{b^{+}(k)}\hat{b(k)})## where ##w_k=\sqrt{{k}.{k}+m^2}## The only non vanishing commutation relations of the creation and annihilation operators are: ## [\alpha(k),\alpha^{+}(p)] =(2\pi)^3...
  19. S

    A Gauge-invariant operators in correlation functions

    Gauge symmetry is not a symmetry. It is a fake, a redundancy introduced by hand to help us keep track of massless particles in quantum field theory. All physical predictions must be gauge-independent...
  20. L

    Hamiltonian in terms of creation/annihilation operators

    Homework Statement Consider the free real scalar field \phi(x) satisfying the Klein-Gordon equation, write the Hamiltonian in terms of the creation/annihilation operators. Homework Equations Possibly the definition of the free real scalar field in terms of creation/annihilation operators...
  21. L

    Partial traces of density operators in the tensor product

    Homework Statement Consider a system formed by particles (1) and (2) of same mass which do not interact among themselves and that are placed in a potential of infinite well type with width a. Let H(1) and H(2) be the individual hamiltonians and denote |\varphi_n(1)\rangle and...
  22. T

    I Hermitian operators, matrices and basis

    Hello, I would just like some help clearing up some pretty basic things about hermitian operators and matricies. I am aware that operators can be represented by matricies. And I think I am right in saying that depending on the basis used the matrices will look different, but all our valid...
  23. Luca_Mantani

    Counting operators with group theory

    Homework Statement I have an exercise that I do not know how to solve. ##N## is a nucleon field, in the fundamental representation of ##SU(4)##. We want to classify operators by their ##SU(4)## transformation properties, bearing in mind that the nucleon is a fermion and we need antisymmetric...
  24. ChrisVer

    C/C++ Understand Bitwise Operators in C++

    Hi guys, I have the following piece of code but I am not sure I understand if I get what it does correctly. static const unsigned int m_nBits = 6; static const unsigned int m_nRanges = 4; max = SOMENUMBER; if( max >= (1 << (m_nBits + m_nRanges - 1) ) ){ doStuff() } In fact I'm trying to...
  25. D

    I Angular momentum raising/lowering operators

    Hi. I have come across the following statement - the eigenvalue equation for J+ is given by J+ | j m > = ħ √{(j+1)-m(m+1)} | j , m+1> My question is this - how can this be an eigenvalue equaton as the ket | j, m> has changed to | j , m+1> ? Surely the raising/lowering operators don't have...
  26. Whiteboard_Warrior

    I Parameterization of linear operators on the holomorphisms

    Let D represent the differentiation of a single-parameter holomorphism, with respect to its parameter x. It's clear that for any sequence of holomorphisms g on x, sigma[k=0,inf](g[k](x)*D^k) is a linear operator on the space of holomorphisms. Is this a complete parameterization of the linear...
  27. redtree

    A Deriving the Lagrangian from the Hamiltonian operator

    In classical mechanics, the Hamiltonian and the Lagrangian are Legendre transforms of each other. By analogy, in quantum mechanics and quantum field theory, the relationship between the Hamiltonian and the Lagrangian seems to be preserved. Where can I find a derivation of the Lagrangian...
  28. TeethWhitener

    I QFT operators time/space asymmetry?

    I'm slowly working through Srednicki's QFT book and I had a question about section 3 (canonical quantization of scalar fields). At one point, he shows that the creation and annihilation operators ##a(\mathbf{k})## and ##a(\mathbf{k}')## are time-independent via the equation: $$a(\mathbf{k})...
  29. K

    A Primaries, descendents and transformation properties in CFT

    I want to clarify the relations between a few different sets of operators in a conformal field theory, namely primaries, descendants and operators that transform with an overall Jacobian factor under a conformal transformation. So let us consider the the following four sets of...
  30. 2

    I Do limit and differential operators commute?

    In general I'm wondering if \lim_{x\to0} \left[\frac{d}{dy} \frac{d}{dx} f(x,y)\right] = \frac{d}{dy} \left[\lim_{x\to0} \frac{d}{dx} f(x,y)\right] holds true for all f(x,y). Thanks.
  31. Karolus

    I Understanding Quantum Operators: Exploring Hermitian Matrices and Degeneracy

    My question is, if I understand the question. For every "observable" physical corresponds a quantum operator. This operator can be represented as an infinite dimensional matrix in a Hilbert space. Only Hermitian matrices each may be quantum mechanical operators, and at the same time to an...
  32. F

    I Are Eigenstates of operators always stationary states?

    Hello everyone, I am wondering if the eigenstates of Hermitian operators, which represent possible wavefunctions representing the system, are always stationary wavefunctions, i.e. the deriving probability distribution function is always time invariant. I would think so since these eigenstates...
  33. N

    I Symmetric, self-adjoint operators and the spectral theorem

    Hi Guys, at the moment I got a bit confused about the notation in some QM textbooks. Some say the operators should be symmetric, some say they should be self-adjoint (or in many cases hermitian what maybe means symmetric or maybe self-adjoint). Which condition do we need for our observables...
  34. Adgorn

    Linear algebra problem: linear operators and direct sums

    Homework Statement Homework Equations N/A The Attempt at a Solution I proved the first part of the question (first quote) and got stuck in the second (second quote). I defined Im(E1) as U and Im(E2) as W and proved that v=u+w where v ∈ V, u ∈ U and w ∈ W. After that however I got stuck at...
  35. E

    I Rotation operators on a sphere, around x and y axis

    I need to start by saying that I'm not a physicist, nor a student of physics. I'm a translator, and my text is about rotations around the azimuthal nodal lines on the sphere. I need to find a name for a particular type of a rotation operator, which rotates the sphere around the x and y axes...
  36. DOTDO

    Ladder operators in electron field and electron's charge

    S. Weinberg says in his book, "The Quantum Theory of Fields Volume I", that Since electrons carry a charge, we would not like to mix annihilation and creation operators, so we might try to write the field as $$\psi(x)=\sum_{k}u_k (x)e^{-i\omega_k t}a_k$$ where ##u_k (x)e^{-i\omega_k t}## are a...
  37. Muthumanimaran

    Do Lindblad Operators Commute?

    Homework Statement Let operator $$\mathcal{L}_{AD}(\rho)$$ and $$\mathcal{L}_{PD}(\rho)$$ is defined as $$\mathcal{L}_{AD}(\rho)=2a\rho{a}^{\dagger}-a^{\dagger}a\rho-\rho{a^{\dagger}}a$$ and $$\mathcal{L}_{PD}(\rho)=2a^{\dagger}a\rho{a^{\dagger}}a-(a^{\dagger}a)^2\rho-\rho(a^{\dagger}a)^2$$...
  38. T

    A Do we need Lindblad operators to describe spontaneous emission

    In Griffith and Sakurai QM book, spontaneous emission is treated as a closed system subject to time-dependent perturbation. Yet in quantum optics sponantanoues emission is treated as in the form master equation of density matrix. Even in two levels system where there is only one spontaneous...
  39. S

    I Harmonic oscillator ladder operators

    The ladder operators of a simple harmonic oscillator which obey $$[H,a^{\dagger}]=\hbar\omega\ a^{\dagger}$$. --- I would like to see a proof of the relation $$\exp(-iHt)\exp(a^{\dagger})\exp(iHt)|0\rangle=\exp(a^{\dagger}e^{-i\omega t})|0\rangle\exp(i\omega t/2).$$ Thoughts?
  40. J

    Argue, why given Operators are compact or not.

    Which of the operators T:C[0,1]\rightarrow C[0,1] are compact? $$(i)\qquad Tx(t)=\sum^\infty_{k=1}x\left(\frac{1}{k}\right)\frac{t^k}{k!}$$ and $$(ii)\qquad Tx(t)=\sum^\infty_{k=0}\frac{x(t^k)}{k!}$$ ideas for compactness of the operator: - the image of the closed unit ball is relatively...
  41. D

    I Integrating imaginary units and operators

    When integrating terms including the imaginary unit i and operators like position and momentum, do you simply treat these as constants?
  42. K

    I Eigenstate of two observable operators

    Let's say you have two operators A and B such that when they act on an eigenstate they yield a measurement of an observable quantity (so they're Hermitian). A and B do not commute, so they can't be measured simultaneously. My question is this: You have a matrix representation of A and B and...
  43. S

    B Operators 'act on' the wavefunction

    The wavefunction describes the state of a system. When an operator 'acts on' the wavefunction are we saying, in layman's terms, that the operator is changing the state of the system?
  44. J

    I Hermitian Operators in QM

    I have been following a series of on-line lectures by Dr Physics A. He clearly describes what Hermitian operators for polarization and spin are and what they do. But when he gets to the position and momentum operators I am rather lost. They are no longer represented by square matrices. The...
  45. H

    I Hermitian Operators in Dirac Equation

    In the dirac equation we have a term which is proportional to \alpha p . In the book they say that \alpha must be an hermitian operator in order for the Hamiltonian to be hermitian. As I understand, we require this because we want (\alpha p)^\dagger = \alpha p. But (\alpha p)^\dagger =...
  46. D

    Understanding Hermitian Operators: Exploring Their Properties and Applications

    Basically I've seen some expressions involving Hermitian Operators that I can't seem to justify, that others on the internet throw around like axiomatic starting points. (AB+BA)+ = (AB)++(BA)+? Why does this work? Assuming A&B are hermitian, I get why we can assume A+B is hermitian, but does...
  47. C

    B States as positive operators of unit trace

    I read that states are positive operators of unit trace - not elements of a vector space. Is it referring to quantum states or all classical states? I know operators are like minus, plus, square root and vectors are like rays in Hilbert space.. but why can't quantum states be vectors when in...
  48. C

    A PDFs expressed as matrix elements of bi-local operators

    Extracted from 'At the frontiers of Physics, a handbook of QCD, volume 2', '...in the physical Bjorken ##x##-space formulation, an equivalent definition of PDFs can be given in terms of matrix elements of bi-local operators on the lightcone. The distribution of quark 'a' in a parent 'X'...
  49. Mayan Fung

    I Exploring the Kinetic Energy Operator: Why is it Differentiated Twice?

    When I learned about operators, I learned <x> = ∫ Ψ* x Ψ dx, <p> = ∫ Ψ* (ħ/i ∂/∂x) Ψ dx. The book then told me the kinetic energy operator T = p2/2m = -ħ2/2m (∂2/∂x2) I am just think that why isn't it -ħ2/2m (∂/∂x)2 Put in other words, why isn't it the square of the derivative, but...
  50. T

    I Are there other types of operators that can produce real eigenvalues?

    I am learning that operators corresponding to observable quantities are Hermitian since the eigenvalues are real. This makes sense (at least intuitively) and I have seen corresponding proofs of why eigenvalues of Hermitian operators are always real. That is fine. But are there any other types of...
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