What is Operators: Definition and 1000 Discussions

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. S

    B Reconciling basis vector operators with partial derivative operators

    Ref. 'Core Principles of Special and General Relativity' by Luscombe. Apologies in advance for the super-long question, but it's necessary to show my thought process. Let ##\gamma:I\to M## be a smooth curve from an open interval ##I\subset\mathbb{R}## to a manifold ##M##, and let...
  2. forever_physicist

    I Quantum operators and trasformation under rotations

    Good morning! I have a problem in understanding the steps from vectors to operators. Imagine you are given a vectorial observable. In classical mechanics, after rotating the system it transform with a rotation matrix R. If we go to quantum mechanics, this observable becomes an operator that is...
  3. AndreasC

    Quantum Hilbert spaces and quantum operators being infinite dimensional matrices

    I just realized quantum operators X and P aren't actually just generalizations of matrices in infinite dimensions that you can naively play with as if they're usual matrices. Then I learned that the space of quantum states is not actually a Hilbert space but a "rigged" Hilbert space. It all...
  4. K

    I Quantum Field Operators for Bosons

    Consider the field creation operator ψ†(x) = ∫d3p ap†exp(-ip.x) My understanding is that this operator does not add particles from a particular momentum state. Rather it coherently (in-phase) adds a particle created from |0> expanded as a superposition of momentum eigenstates states...
  5. E

    B Question about squares of operators

    The magnitude of the momentum ##p## satisfies ##p^2 = p_x^2 + p_y^2 + p_z^2## and this implies the operator equation ##\hat{p}^2 = \hat{p}_x^2 + \hat{p}_y^2 + \hat{p}_z^2##, so we can say that ##\hat{p}^2 = -\hbar^2 (\frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} +...
  6. K

    I Finding matrices of perturbation using creation/annihilation operators

    "Given a 3D Harmonic Oscillator under the effects of a field W, determine the matrix for W in the base given by the first excited level" So first of all we have to arrange W in terms of the creation and annihilation operator. So far so good, with the result: W = 2az2 - ax2 - ay2 + 2az+ 2 -ax+...
  7. Tanmoy

    Annihilation operators of two different types of Fermions

    IfA=cd, where c and d are annihilation operators of two different types of Fermions, then {A,A°}is? A.1+n1+n2 B.1-n1+n2 C.1-n2+n1 D.1-n1-n2 Where,n1 and n2 are corresponding number operator, A° means A dagger or creation operator,as the particles are fermions they will obey anti-commutation I think
  8. Q

    A Algebraic form of Klein Gordon ##\phi^4## vacuum and ladder operators

    In theory, does an algebraic expression exist for the ground state of the Klein Gordon equation with \phi^4 interactions in the same way an algebraic expression exists for the simple harmonic oscillator ground state wavefunction in Q.M.? Is it just that it hasn't been found yet or is it...
  9. Antarres

    I Creation/annihilation operators question

    I've recently stumbled upon something that looked kind of silly, but I still find myself a bit confused by it. Namely in quantum field theory, when we quantize a scalar field, we impose commutation relations on creation and annihilation operators that correspond to momenta in their mode...
  10. JD_PM

    Working out harmonic oscillator operators at ##L \rightarrow \infty##

    Let's go step by step a) We know that the harmonic oscillator operators are $$a^{\dagger} = \frac{1}{\sqrt{2 \hbar m \omega}} ( -ip + m \omega q)$$ $$a= \frac{1}{\sqrt{2 \hbar m \omega}} (ip + m \omega q)$$ But these do not depend on ##L##, so I guess these are not the expressions we want...
  11. T

    A Exploring the Conditions for Evaluating Commutators with Fermionic Operators

    I found a theorem that states that if A and B are 2 endomorphism that satisfies $$[A,[A,B]]=[B,[A,B]]=0$$ then $$[A,F(B)]=[A,B]F'(B)=[A,B]\frac{\partial F(B)}{\partial B}$$. Now I'm trying to apply this result using the creation and annihilation fermionics operators $$B=C_k^+$$ and $$A=C_k$$...
  12. JD_PM

    A Commutation relations between HO operators | QFT; free scalar field

    I am getting started in applying the quantization of the harmonic oscillator to the free scalar field. After studying section 2.2. of Tong Lecture notes (I attach the PDF, which comes from 2.Canonical quantization here https://www.damtp.cam.ac.uk/user/tong/qft.html), I went through my notes...
  13. G

    Harmonic Oscillator Ladder Operators - What is (ahat_+)^+?

    I know that ahat_+ = 1/sqrt((2*m*h_bar*w)) * (mw(xhat)+i(phat)) and ahat_- = 1/sqrt((2*m*h_bar*w)) * (mw(xhat)-i(phat)). But I'm not sure what (ahat_+)^+ could be.
  14. cookiemnstr510510

    Linear operators, quantum mechanics

    Hello, I am struggling with what each piece of these equations are. I generally know the two rules that need to hold for an operator to be linear, but I am struggling with what each piece of each equation is/means. Lets look at one of the three operators in question. A(f(x))=(∂f/∂x)+3f(x) I...
  15. G

    I Is there a reason eigenvalues of operators correspond to measurements?

    Given a wave function \Psi which is an eigenstate of a Hermitian operator \hat{Q}, we can measure a definite value of the observable corresponding to \hat{Q}, and the value of this observable is the eigenvalue Q of the eigenstate $$ \hat{Q}\Psi = Q\Psi $$ My question is whether it's a postulate...
  16. Y

    Deriving commutator of operators in Lorentz algebra

    Li=1/2*∈ijkJjk, Ki=J0i,where J satisfy the Lorentz commutation relation. [Li,Lj]=i/4*∈iab∈jcd(gbcJad-gacJbd-gbdJac+gadJbc) How can I obtain [Li,Lj]=i∈ijkLk from it?
  17. A

    I Raising and Lowering Operators

    Why is it that the raising and lowering operators in a spin 1/2 system have a factor of $\hbar ?$ From Sakurai: $$S_+ \equiv \hbar | + \rangle \langle - |, S_- \equiv \hbar | - \rangle \langle + |$$ "So the physical interpretation of $S_+$ is that it raises the component by one unit of $\hbar...
  18. Garlic

    Landau levels: Hamiltonian with ladder operators

    Dear PF, I hope I've formulated my question understandable enough. Thank you for your time, Garli
  19. Q

    A Do the time and normal ordering operators commute?

    Does the time ordering operator ##\mathcal{T}## commute with the normal ordering operator ##\hat{N}##? i.e. is $$[ \mathcal{T},\hat{N}] =0$$ correct?
  20. Abhishek11235

    I Condition for delta operator and total time differential to commute

    While deriving continuity equation in Fluid mechanics, our professor switched the order of taking total time derivative and then applying delta operator to the function without stating any condition to do so(Of course I know it is Physics which alows you to do so) . So,I began to think...
  21. J

    A Creation/annihilation operators and trigonometric functions

    Hello everyone, I have noticed a striking similarity between expressions for creation/annihilation operators in terms position and momentum operators and trigonometric expressions in terms of exponentials. In the treatment by T. Lancaster and S. Blundell, "Quantum Field Theory for the Gifted...
  22. W

    I Hermitian operators in QM and QFT

    I have always learned that a Hermitian operator in non-relativistic QM can be treated as an "experimental apparatus" ie unitary transformation, measurement, etc. However this makes less sense to me in QFT. A second-quantised EM field for instance, has field operators associated with each...
  23. Q

    A Explicit form of annihilation and creation operators for Dirac field

    I'm unclear on what exactly an annihilation or creation operator looks like in QFT. In QM these operators for the simple harmonic oscillator had an explicit form in terms of $$ \hat{a}^\dagger = \frac{1}{\sqrt{2}}\left(- \frac{\mathrm{d}}{\mathrm{d}q} + q \right),\;\;\;\hat{a} =...
  24. MichPod

    I Why observables are represented as operators in QM?

    Can somebody provide an explanation why the dynamical variables/observables are represented in QM as linear operators with the measured values being eigenvalues of these operators? For energy this is probably trivially and directly follows from the stationary Shrodinger equation which solutions...
  25. A

    I Understanding Operators in Matrix Mechanics

    I'm trying to understand some notes that I have been given on Matrix Mechanics, specifically how the matrix element comes about and builds a matrix which when used applies the effect of an operator on a wavefunction. But I'm having some difficulties following what's being done in the notes with...
  26. Pencilvester

    I Multiplying two function operators

    I am reading Zettili’s “Quantum Mechanics: Concepts and Applications” and I am in the section on functions of operators. It starts with how ##F(\hat A)## can be Taylor expanded and gives the particular and familiar example: $$e^{a \hat A} = \sum_{n=0}^\infty \frac{a^n}{n!} \hat A^n...
  27. K

    I Boundary terms for field operators

    Hello! In several of the derivations I read so far in my QFT books (M. Schawarz, Peskin and Schroeder) they use the fact that "we can safely assume that the fields die off at ##x=\pm \infty##" in order to drop boundary terms. I am not sure I understand this statement in terms of QFT. A field in...
  28. P

    I Quantum Computing - projection operators

    Assume ##P_1## and ##P_2## are two projection operators. I want to show that if their commutator ##[P_1,P_2]=0##, then their product ##P_1P_2## is also a projection operator. My first idea was: $$P_1=|u_1\rangle\langle u_1|, P_2=|u_2\rangle\langle u_2|$$ $$P_1P_2= |u_1\rangle\langle...
  29. E

    Expectation value of operators and squeezing in the even cat state

    I started and successfully showed that the expectation of X_1 and X_2 are zero. However the expectation value of X1^2 and X2^2 which I am getting is <X1^2> = 0.25 + \alpha^2 and <X2^2> = 0.25. How do I derive the given equations?
  30. Gbox

    Ladder Operators: Commutation Relation & Beyond

    a. ##L_{+}^{\dagger}=(L_x+iL_y)^{\dagger}=L_x-iL_y=L_{-}## b.##[L_{+},L_{-}]=[L_x+iL_y,L_x-iL_y]=(L_x+iL_y)(L_x-iL_y)-(L_x-iL_y)(L_x+iL_y)=## ##=L_x^2-iL_xL_y+iL_yL_x+L_y^2-(L_x^2+iL_xL_y-iL_yL_x-L_y^2)## ##=L_x^2-iL_xL_y+iL_yL_x+L_y^2-L_x^2-iL_xL_y+iL_yL_x+L_y^2##...
  31. muonion

    I Do spin operators 'appear' to commute for an entangled spin state?

    Let's consider Bohm's paradox (explaining as follows). A zero spin particle converts into two half-spin particles which move in the opposite directions. The parent particle had no angular momentum, so total spin of two particles is 0 implying they are in the singlet state. Suppose we measured Sz...
  32. R

    I Projection Operators: Pi, Pj, δij in Quantum Mechanics

    In Principles of Quantum mechanics by shankar it is written that Pi is a projection operator and Pi=|i> <i|. Then PiPj= |i> <i|j> <j|= (δij)Pj. I don't understand how we got from the second result toh the third one mathematically.I know that the inner product of i and j can be written as δijbut...
  33. T

    I Derivative operators in Galilean transformations

    I'm studying how derivatives and partial derivatives transform under a Galilean transformation. On this page: http://www.physics.princeton.edu/~mcdonald/examples/wave_velocity.pdf Equation (16) relies on ##\frac{\partial t'}{\partial x}=0## but ##\frac{\partial x'}{\partial t}=-v## But this...
  34. J

    I Pauli exclusion principle and Hermitian operators

    http://vergil.chemistry.gatech.edu/notes/quantrev/node20.html "Postulate 2. To every observable in classical mechanics there corresponds a linear, Hermitian operator in quantum mechanics. " "Postulate 6. The total wavefunction must be antisymmetric with respect to the interchange of all...
  35. Mutatis

    Show the formula which connects the adjoint representations

    That's my attempting: first I've wrote ##e## in terms of the power series, but then I don't how to get further than this $$ \sum_{n=0}^\infty (-1)^n \frac {Â^n} {n!} \hat B \sum_{n=0}^\infty \frac {Â^n} {n!} = \sum_{n=0}^\infty (-1)^n \frac {Â^2n} {\left( n! \right) ^2} $$. I've alread tried to...
  36. C

    Hermitian operators in quantum gravity

    Are there new hermitian operators in quantum gravity? Background: In many worlds interpretation (MWI). We have the preferred basis problem and the basis are for example position, momentum, spin. Each of those bases come from a hermitian operator: they are the eigenbasis of the (for example)...
  37. Haorong Wu

    The position and momentum operators for a free particle in Heisenberg picture

    Homework Statement From Griffiths GM 3rd p.266 Consider a free particle of mass ##m##. Show that the position and momentum operators in the Heisenberg picture are given by$$ {\hat x}_H \left( t \right) ={\hat x}_H \left( 0 \right) + \frac { {\hat p}_H \left( 0 \right) t} m $$ $$ {\hat p}_H...
  38. jdou86

    I Confusion about the Concept of Operators

    Dear all, I've been reading and got confused of the concept below have two questions question 1) For <ψ|HA|ψ> = <Hψ|A|ψ>, why does the Hamiltonian operator acting on the bra state and <ψ|AH|ψ> in this configuration it will act on the ket state? question 2) what does it mean for H|ψ> = |Hψ>...
  39. A

    A Manipulations with Hubbard operators

    Hi, I'm starting to study how to use Hubbard operators and I cannot understand one property: Consider the hopping terms for a lattice Hamiltonian with bosons: $$\sum_{i,j\neq i} t_{i,j} b^\dagger_i b_j$$ when writing this term in the basis of Hubbard operators $$X^{a,b}_i =| a,i \rangle \langle...
  40. L

    I Symmetries in quantum mechanics and the change of operators

    When we make a symmetrie transformation in a quantum system, the state ##|\psi \rangle## change to ## |\psi' \rangle = U|\psi \rangle##, where ##U## is a unitary or antiunitary operator, and the operator ##A## change to ##A'##. If we require that the expections values of operators don't change...
  41. S

    If A and B are Hermitian operators is (i A + B ) Hermitian?

    If A and B are Hermitian operators is (i A + B ) a Hermitian operator? (Hint: use the definition of hermiticity used in the vector space where the elements are quadratic integrable functions) I know an operator is Hermitian if: - the eigenvalues are real - the eigenfunction is orthonormal -...
  42. TheBigDig

    Spin Annhilation and Creator Operators Matrix Representation

    Homework Statement Given the expression s_{\pm}|s,m> = \hbar \sqrt{s(s+1)-m(m\pm 1)}|s,m \pm 1> obtain the matrix representations of s+/- for spin 1/2 in the usual basis of eigenstates of sz Homework Equations s_{\pm}|s,m> = \hbar \sqrt{s(s+1)-m(m\pm 1)}|s,m \pm 1> S_{+} = \hbar...
  43. G

    I Annihilation vs. Creation Operators: What's the Difference?

    Cohererent states are defined as eigenstates of the annihilation operator. Never the creation operator is referred to. Is this just a convention or is more behind? What is the essential difference between eigenstates of the annihilation- versus the creation operator? Thank you very much in...
  44. P

    I Multiplication of ladder-operators

    Hi! When calculating ##(\hat{a} \hat{a}^{\dagger})^2## i get ##\hat{a} \hat{a} \hat{a}^{\dagger} \hat{a}^{\dagger}## which is perfectly fine. But how do I end up with the ultimate simplified expression $$\hat{ a}^{\dagger} \hat{a} \hat{a}^{\dagger} \hat{a} + \hat{a}^{\dagger} \hat_{a} +...
  45. Hiero

    B Gradient and divergence operators

    One way to get the gradient of polar coordinates is to start from the Cartesian form: ##\nabla = \hat x \frac{\partial}{\partial x} + \hat y \frac{\partial}{\partial y}## And then to use the following four identies: ##\hat x = \hat r\cos\theta - \hat{\theta}\sin\theta## ##\hat y = \hat...
  46. M

    I Raising the ladder operators to a power

    Hi! I am working on homework and came across this problem: <n|X5|n> I know X = ((ħ/(2mω))1/2 (a + a+)) And if I raise X to the 5th, its becomes X5 = ((ħ/(2mω))5/2 (a + a+)5) What I'm wondering is, is there anyway to be able to solve this without going through all of the iterations the...
  47. Technon

    A Operators used without being explained

    I started watching the video lecture series here: https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2016/video-lectures/part-1/ I notice that they use the term "operator" without first explaining it. Operators are also not explained (in fact they are not even mentioned) in my...
  48. A

    I Does a Quantum Field Creation Operator Create Particles at a Given Location?

    Hi, It appears that the definition of a quantum field creation operator is given by $$\Psi^{\dagger}(\mathbf r) = \sum\limits_{\mathbf k} e^{-i\mathbf k\cdot \mathbf r} a^{\dagger}_{\mathbf k}.$$ But then if we examine how this operator acts on the vacuum state, we get $$\Psi^{\dagger}(\mathbf...
  49. astrocytosis

    Prove formula for the product of two exponential operators

    Homework Statement Consider two operators A and B, such that [A,[A, B]] = 0 and [B,[A, B]] = 0 . Show that Exp(A+B) = Exp(A)Exp(B)Exp(-1/2 [A,B]) Hint: define Exp(As)Exp(Bs) as T(s), where s is a real parameter, differentiate T(s) with respect to s, and express the result in terms of T(s)...
  50. Paul Colby

    I Gluon creation and annihilation operators

    Hi, When one quantizes EM the resulting gauge boson, the photon, ends up being its own antiparticle. From what I read of gluons, they have anti particles. I can follow how anti particles come about quantizing a complex-valued field like that for electrons. For the spin 1/2 case non-interacting...
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