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

    A Annihilation creation operators in case of half H.oscillator

    I'm trying to check if Ehrenfest theorem is satisfied for this wave function, |Y>=(1/sqrt(2))*(|1>+|3>), where |1> and |3> are the ground and 1st exited state wave functions of a half harmonic oscillator. When I'm calculating the expectation values of x and p using annihilation creation...
  2. sams

    I Hermitian operators in quantum mechanics

    Hello everyone, There's something I am not understanding in Hermitian operators. Could anyone explain why the momentum operator: px = -iħ∂/∂x is a Hermitian operator? Knowing that Hermitian operators is equal to their adjoints (A = A†), how come the complex conjugate of px (iħ∂/∂x) = px...
  3. gasar8

    Angular momentum operators on a wave function

    Homework Statement Particle is in a state with wave function \psi (r) = A z (x+y)e^{-\lambda r}. a) What is the probability that the result of the L_z measurement is 0? b) What are possilble results and what are their probabilities of a L^2 measurement? c) What are possilble results and what...
  4. ShayanJ

    A Problem with fields and operators in holographic duality

    I'm reading McGreevy's lecture notes on holographic duality but I have two problems now: (See here!) 1) The author considers a matrix field theory for large N expansion. At first I thought its just a theory considered as a simple example and has nothing to do with the ## \mathcal N=4 ## SYM...
  5. A

    Matrix representation of certain Operator

    Homework Statement Vectors I1> and I2> create the orthonormal basis. Operator O is: O=a(I1><1I-I2><2I+iI1><2I-iI2><1I), where a is a real number. Find the matrix representation of the operator in the basis I1>,I2>. Find eigenvalues and eigenvectors of the operator. Check if the eigenvectors are...
  6. F

    I Question about commuting operators

    Hi everybody. I have a (I gess rather silly) question. If I define [Jk,Ll]=iħΣmεklmLm, what would happen if I made [J, L]?. I gess it would be iħΣjεiijLi=0. Can someone please confirm this? Thanks for reading.
  7. orion

    I Do derivative operators act on the manifold or in R^n?

    I am really struggling with one concept in my study of differential geometry where there seems to be a conflict among different textbooks. To set up the question, let M be a manifold and let (U, φ) be a chart. Now suppose we have a curve γ:(-ε,+ε) → M such that γ(t)=0 at a ∈ M. Suppose further...
  8. weezy

    I What is a time-dependent operator?

    While studying Ehrenfest's theorem I came across this formula for time-derivatives of expectation values. What I can't understand is why is position/momentum operator time-independent? What does it mean to be a time-dependent operator? Since position/momentum of a particle may change...
  9. F

    I Kronecker delta by using creation/annihilation operators

    Hey all, i've found the following expression: How do they get that? They somehow used the kronecker delta Sum_k exp(i k (m-n))=delta_mn. But in the expression above, they're summing over i and not over r_i?? Best
  10. Xico Sim

    I Quarks and isospin ladder operators

    Hi, guys. This is actually a question about quantum mechanics, but since the context in which it appeared is particle physics, I'll post it here. On Thompson's book (page 227, equation (9.32)), we have $$T_+ |d\bar{u}\rangle = |u\bar{u}\rangle - |d\bar{d}\rangle$$ But I thought...
  11. S

    I Sum of squares of 2 non-commutating operators

    Prof Adams does something rather strange, starting from 14:35 minutes in this lecture -- http://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2013/lecture-videos/lecture-9/ He reminds us that for complex scalars, ##c^2+d^2=(c-id)(c+id)## and then proceeds to do the same with...
  12. D

    A Time dependence of field operators

    In field theory we most of deal with theories whose Lagrangian densities are of the form (sticking to scalar fields for simplicity) $$\mathcal{L}= -\frac{1}{2}\partial_{\mu}\phi\partial^{\mu}\phi - \frac{1}{2}m_{\phi}^{2}\phi^{2} + \cdots$$ where ##\partial := \frac{\partial}{\partial x^{\mu}}##...
  13. bananabandana

    How Does Time Evolution Affect Quantum Operator Matrix Elements?

    Homework Statement [/B] For a general operator ## \hat{O}##, let ##\hat{O}_{mn}(t)## be defined as: $$ \hat{O_{mn}}(t) = \int u^{*}_{m}(x,t) \hat{O} u_{n}(x,t) $$ and $$ \hat{O_{mn}} = \int u^{*}_{m}(x) \hat{O} u_{n}(x) $$ ##u_{m}## and ##u_{n}## are energy eigenstates with corresponding...
  14. J

    A Form factor and new EFT operators for a WIMP on a nucleon

    Hi, On the third paragraph(right column) of page 1 of the paper, http://journals.aps.org/prc/pdf/10.1103/PhysRevC.89.065501 , It says on form factor, "Because the momentum transfer in the scattering is large compared to the inverse nuclear size, form factors are generally included ". I...
  15. Harry Smith

    I Why does a sum of operators act on the state like this?

    I'm reading through my quantum physics lecture notes (see page 216 of the lecture notes for more details) and under the ladder operators section there is a discussion of the expectation value of ##L_x## for a state ##\psi = R(r) \left( \sqrt{ \frac{2}{3}} Y_{11} - \sqrt{ \frac{1}{3}} Y_{10}...
  16. S

    I Second quantization and creation/annih. operators

    I'd like some help with something in this introduction to second quantization ... http://yclept.ucdavis.edu/course/242/Class.html They start by considering two operators ##a## and ##a^\dagger## such that ##[a,a^\dagger]=1## and they are adjoint to each other. Also introduced is a state...
  17. C

    A Time-ordering fermion operators

    If A and B are fermionic operators, and T the time-ordering operator, then the standard definition is T(AB) = AB, if B precedes A = - BA, if A precedes B. Why is there a negative sign? If A and B are space-like separated then it makes sense to assume that A and B anticommute. But...
  18. D

    I Exponential Operators: Inverting, Rearranging, Expanding

    If I rearrange an equation invoving exponentials of operators and I take ex to the opposite side of the equation it becomes e-x. What happens if I try to take eA to the opposite side ? I know a exponential of operators can be expanded as a Taylor series which involves products of matrices but...
  19. S

    A Commutation relations - field operators to ladder operators

    I would like to show that the commutation relations ##[a_{\vec{p}},a_{\vec{q}}]=[a_{\vec{p}}^{\dagger},a_{\vec{q}}^{\dagger}]=0## and ##[a_{\vec{p}},a_{\vec{q}}^{\dagger}]=(2\pi)^{3}\delta^{(3)}(\vec{p}-\vec{q})## imply the commutation relations...
  20. Ackbach

    MHB Different Kinds of Quantum Computing Measurement Operators

    So in quantum mechanics, there are at least three different kinds of measurement operators: the General, the Projective, and the Positive Operator-Valued (POVM). They have different properties and relationships. In a typical QM book, these are not delineated, but in Quantum Computing they are...
  21. F

    I Inner products and adjoint operators

    I'm trying to prove the following relation $$\langle\psi\lvert \hat{A}^{\dagger}\rvert\phi\rangle =\langle\phi\lvert \hat{A}\rvert\psi\rangle^{\ast}$$ where ##\lvert\phi\rangle## and ##\lvert\phi\rangle## are state vectors and ##\hat{A}^{\dagger}## is the adjoint of some operator ##\hat{A}##...
  22. QuantumRose

    Commutator relations of field operators

    Here is the question: By using the equality (for boson) ---------------------------------------- (1) Prove that Background: Currently I'm learning things about second quantization in the book "Advanced Quantum Mechanics"(Franz Schwabl). Given the creation and annihilation operators(), define...
  23. aboutammam

    A About diagonalisation of shape operators

    Dear fiends, I have a question if it possible, Given a submanifold Mⁿ of codimensioon p in a riemannian manifold N^{n+p}. Let (e₁,...,e_{p}) an orthonormal basis of the notmal vector space of Mⁿ in M^{n+p}. For every e_{i} we can define the shape opeator A_{e_{i}} of the second...
  24. P

    Representing spin operators in alternate basis

    Homework Statement I want to find the matrix representation of the ##\hat{S}_x,\hat{S}_y,\hat{S}_z## and ##\hat{S}^2## operators in the ##S_x## basis (is it more correct to say the ##x## basis, ##S_x## basis or the ##\hat{S}_x## basis?). Homework Equations...
  25. C

    I Raising and lowering operators for a composite isospin SU(2)

    Consider pion states composed of ##q \bar q## pairs where ##q \in \left\{u,d \right\}## transforms under an ##SU(2)## isospin flavour symmetry. These bound states transform in the tensor product ##R_1 \otimes R_2## of two representations ##(R_1, R_2)## of ##SU(2)##. Take ##R_2## as the...
  26. Raptor112

    Commuting Operators: Understanding How M1,M2 & M3 Work Together

    Homework Statement It is known that ##M_1,M_2, M_3## commute with each other but I don't see how the second line is achieved even though it says that it's using that ##M_1## and ##M_2## commute?
  27. L

    Similarity Transformation Involving Operators

    Homework Statement Virtually all quantum mechanical calculations involving the harmonic oscillator can be done in terms of the creation and destruction operators and by satisfying the commutation relation \left[a,a^{\dagger}\right] = 1 (A) Compute the similarity transformation...
  28. Ernesto Paas

    I When can one clear the operator

    Hi all! I'm having problems understanding the operator algebra. Particularly in this case: Suppose I have this projection ## \langle \Phi_{1} | \hat{A} | \Phi_{2} \rangle ## where the ##\phi's ## have an orthonormal countable basis. If I do a state expansion on both sides then I suppose I'd get...
  29. davidbenari

    I If operators commute then eigenstates are shared

    I'm confused about the statement that if operators commute then eigenstates are shared. My main confusion is this one: ##L^2## commutes with ##L_i##. Then these two share eigenstates. But ##L_x## and ##L_y## do not commute, so they don't share eigenstates. Isn't this violating some type of...
  30. C

    Quantum operators and commutation relations

    Homework Statement Given the mode expansion of the quantum field ##\phi## and the conjugate field one can derive $$\mathbf P = \int \frac{d^3 \mathbf p}{(2\pi)^3 2 \omega(\mathbf p)} \mathbf p a(\mathbf p)^{\dagger} a(\mathbf p)$$ By writing $$e^X = \text{lim}_{n \rightarrow \infty}...
  31. T

    I Non-commuting operators on the same eigenfunctions

    In Griffiths chapter 4 (pg. 179-180) there is an example (Ex. 4.3) that details the expectation value of ## S_x ##, ##S_y##, and ##S_z## of a spin 1/2 particle in a magnetic field. In this example, they find an eigenvector of ## H## (which commutes with ## S_z##) but then use this same...
  32. G

    Diagonalizing a polynomial of operators (Quantum Mechanics)

    The problem asks for the diagonalization of (a(p^2)+b(x^2))^n, where x and p are position and momentum operators with the commutation relation [x,p]=ihbar. a and b are real on-zero numbers and n is a positive non-zero integer.I know that it is not a good way to use the matrix diagonalization...
  33. pellman

    I Aren't all linear operators one-to-one and onto?

    Let W be a vector space and let A be a linear operator W --> W. Isn't it the case that for any such A, the kernel of A is the zero vector and the range is all of W? And that it is one-to-one from linearity? I ask because an author I am reading goes through a lot of steps to show that a certain...
  34. DrPapper

    I Expression for Uncertainty of Arbitrary Operator

    Hello all, as far as I can see this question is not posted already, my apologies if it is and please provide a link. But I'm watching this video on youtube: And at 22:38 there's an expression given for the uncertainty of an arbitrary operator Q, however I'm concerned the expression is incorrect...
  35. Z

    I How exactly does squaring operators (e.g. <p^2> work?

    I'm having to essentially piece together a framework of background knowledge to understand parts of a QM class in which I'm lacking prerequisites; one of the things that I noticed that really confused me was the square of the momentum operator <p>, and how that translated into the integrand of...
  36. askhetan

    Understanding operators for Green's function derivation

    Dear All, I am trying to understand what operators actually mean when deriving the definition of green's function. Is this integral representation of an operator in the ##x-basis## correct ? ## D = <x|\int dx|D|x>## I am asking this because the identity operator for non-denumerable or...
  37. L

    Eigenstates of Orbital Angular Momentum

    Recently I've been studying Angular Momentum in Quantum Mechanics and I have a doubt about the eigenstates of orbital angular momentum in the position representation and the relation to the spherical harmonics. First of all, we consider the angular momentum operators L^2 and L_z. We know that...
  38. phys-student

    Finding expectation values for given operators

    Homework Statement The Hamiltonian of an electron in solids is given by H. We know that H is an Hermitian operator, it satisfies the following eigenvalue equation: H|Φn> = εn|Φn> Let us define the following operators in terms of H as: U = e^[(iHt)/ħ] , S = sin[(Ht)/ħ] , G = (ε -...
  39. J

    Raising and Lowering Operators

    In Griffith and Shankar, the raising and lowering operator seem to appear from nowhere, but it seems really elegant. Where do they come from, is it some corollary from certain mathematical structure? Can anyone give a brief explanation?
  40. B

    Do ladder operators give integer multiples of ћ?

    Say I apply a raising operator to the spin state |2,-1>, then by using the the equation S+|s,ms> = ћ*sqrt(s(s+1) - ms(ms+1))|s,ms+1> I get, S+|2,-1> = sqrt(6)ћ|2,0> Does this correspond to a physical eigenvalue or should I disregard it and only take states with integer multiples of ћ as...
  41. amjad-sh

    Hermitian Operators: Understanding How They Work

    We know that operators can be represented by matrices. Every operator in finite-dimensional space can be represented by a matrix in a given basis in this space. If the transpose conjugate of the matrix representation of an operator in a given basis is the same of the original matrix...
  42. Raptor112

    Matrix Representation for Combined Ladder Operators

    Due to the definition of spin-up (in my project ), \begin{eqnarray} \sigma_+ = \begin{bmatrix} 0 & 2 \\ 0 & 0 \\ \end{bmatrix} \end{eqnarray} as opposed to \begin{eqnarray} \sigma_+ = \begin{bmatrix} 0 & 1 \\ 0 & 0 \\ \end{bmatrix} \end{eqnarray} and the annihilation operator is...
  43. samjohnny

    Spin Angular Momentum and Operators

    Homework Statement Attached Homework Equations ##J_+|j,m⟩ = ћ\sqrt{j(j+1)-m(m+1)} |j,m+1⟩## ##J_-|j,m⟩ = ћ\sqrt{j(j+1)-m(m-1)} |j,m-1⟩## ##J_z|j,m⟩ = mћ |j,m⟩## ##J^2|j,m⟩ = ћ^2j(j+1) |j,m⟩## The Attempt at a Solution Hi there, For part a, the expression we're looking for is given, but...
  44. M

    Harmonic Oscillator and Ladder Operators

    Homework Statement Consider a linear harmonic oscillator with the solution defined by the ladder operators a and a†. Use the number basis |n⟩ to do the following. a) Construct a linear combination of |0⟩ and |1⟩ to form a state |ψ⟩ such that ⟨ψ|X|ψ⟩ is as large as possible. b) Suppose that...
  45. H

    Matrix representation of operators

    Let the operators ##\hat{A}## and ##\hat{B}## be ##-i\hbar\frac{\partial}{\partial x}## and ##x## respectively. Representing these linear operators by matrices, and a wave function ##\Psi(x)## by a column vector u, by the associativity of matrix multiplication, we have...
  46. H

    Why is (5.302) an Approximation of Exponential Operators?

    Why is (5.302) an approximation instead of an equality? Let ##T## be the operator ##\frac{p_x^2}{2m}##. By the law of indices, we should have ##e^{-\frac{i}{\hbar}(T+V)\Delta t}=e^{-\frac{i}{\hbar}T\Delta t} e^{-\frac{i}{\hbar}V\Delta t}## exactly. Is it because ##T## and ##V## do not commute...
  47. Ackbach

    MHB Quantum Computing: Positive Operators are Hermitian

    Exercise 2.24 on page 71 of Nielsen and Chuang's Quantum Computation and Quantum Information asks the reader to show that a positive operator is necessarily Hermitian. There is a hint given; namely, that you first show an arbitrary operator can be written $A=B+iC$, where $B$ and $C$ are...
  48. Q

    Ceiling and floor operators used for min max

    I remember seeing somewhere people using symbols for ceiling and floor operators together with super/subscripts as substitutes for min and max. Example: \lceil x \rceil ^k to mean min(x,k). Has anyone ever seen this? Where? Thanks!
  49. MAGNIBORO

    This hypothesis is right about operators on convergent and divergent series?

    Sorry for the bad English , do not speak the language very well. I posted this to know if the statement or " hypothesis " is correct . thank you very much =D. First Image:https://gyazo.com/7248311481c1273491db7d3608a5c48e Second Image:https://gyazo.com/d8fc52d0c99e0094a6a6fa7d0e5273b6 Third...
  50. JaredMTg

    Eigenfunction of multiple operators simultaneously?

    Hello, I am taking an introductory course in quantum mechanics. One thing I am confused about is, Schrodinger's equation seems to be regarded as the "ultimate" formula which determines a particle's possible wavefunctions and energies, given a certain potential (Hamiltonian of psi = Energy...
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