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. J

    Discrepancy in Lagrangian to Hamiltonian transformation?

    I know, $$ L=T-V \;\;\; \; \;\;\; [1]\;\;\; \; \;\;\; ( Lagrangian) $$ $$ H=T+V \;\;\; \; \;\;\;[2] \;\;\; \; \;\;\; (Hamiltonian)$$ and logically, this leads to the equation, $$ H - L= 2V \;\;\; \; \;\;\...
  2. J

    Self adjoint operators in spherical polar coordinates

    Hi, I have a general question. How do I show that an operator expressed in spherical coordinates is self adjoint ? e.g. suppose i have the operator i ∂/∂ϕ. If the operator was a function of x I know exactly what to do, just check <ψ|Qψ>=<Qψ|ψ> But what about dr, dphi and d theta
  3. Biker

    I Using Differential operators to solve Diff equations

    I don't really understand how their inverses work. For example, in solving 2nd order linear non-homogeneous differential equations. The particular solution is found by ## y_{pi} = \frac{p(x)}{f(D)} ## And they continue by expanding using maclaurin series. How do you treat an operator as a...
  4. Another

    I Question about Operators in Quantum Mechanics

    I study on quantum mechanics and I have question about operator. In one dimension. How do we know ## \hat{x} = x## and ## \hat{p}_{x} = -i \bar{h} \frac{d}{dx} ## When schrodinger was creating an equation, which later called "the schrodinger equation". How does he know momentum operator equal...
  5. K

    I Ladder operators and SU(2) representation

    Hello! I read in many places the derivation of the representation for SU(2) using ladder operators and in all of the places they say that, due to the fact that we are looking for a finite dimensional representation, the ladder must end at a point, hence why we have an eigenvector of ##L_3##...
  6. P

    Eigenfunction of momentum and operators

    Homework Statement Homework Equations ##\hat{P}= -ih d/dx## The Attempt at a Solution To actually obtain ##\psi_{p_0}## I guess one can apply the momentum operator on the spatial wavefunction. If we consider a free particle (V=0) we can easily get obtain ##\psi = e^{\pm i kx}##, where ##k=...
  7. RicardoMP

    Bosonic annihilation and creation operators commutators

    Homework Statement After proving the relations ##[\hat{b}^{\dagger}_i,\hat{b}^{\dagger}_j]=0## and ##[\hat{b}_i,\hat{b}_j]=0##, I want to prove that ##[\hat{b}_j,\hat{b}^{\dagger}_k]=\delta_{jk}##, however I'm not sure where to begin. 2. The attempt at a solution I tried to apply the...
  8. J

    Eigenketes and Eigenvalues of operators

    Homework Statement Again, consider the two-dimensional vector space, with an orthonormal basis consisting of kets |1> and |2>, i.e. <1|2> = <2|1> = 0, and <1|1> = <2|2> = 1. Any ket in this space is a linear combination of |1> and |2>. a) [2pt] The operator A acts on the basis kets as A|1> =...
  9. Sophrosyne

    B Creation and annihilation operators in particle physics

    I was recently reading about annihilation and creation operators in particle physics using the model of an harmonic oscillator, and then quantizing it. This is fine. I can understand it. But how does this quantization of the energy of the harmonic oscillator manifest physically? Is it that only...
  10. LarryC

    Simultaneous Diagonalization for Two Self-Adjoint Operators

    (a) and (b) are fairly traditional, but I have trouble understanding the phrasing of (c). What makes the infinite dimensionality in (c) different from (a) and (b)?
  11. M

    Creation and Annihilation operators on photons

    Homework Statement The possible (normalized) eigenstates of a photon in a given system are written as: $$|\psi_1>,|\psi_2>,...|\psi_m>$$ Let another state be $$|\phi> = \frac{|\psi_1>+|\psi_2>+...+|\psi_m>}{\sqrt{m}}$$ and denote: $$|n>=|\psi_1>|\psi_1>...|\psi_1>$$ which represent a state...
  12. S

    I Commuting set of operators (misunderstanding)

    I don’t see how the definition of |an> transmorphs into the statement involving the kroneck delta functions.
  13. hideelo

    A Does an irreducible representation acting on operators imply....

    Ok, so my question is "Does an irreducible representation acting on operators imply that the states also transform in an irreducible representation?" and what I mean by that is the following. If I have an operator transforming in an irreducible transformation of some group, I get a corresponding...
  14. Mutatis

    Write the matrix representation of the raising operators....

    Homework Statement Hi, guys. The question is: For a 3-state system, |0⟩, |1⟩ and |2⟩, write the matrix representation of the raising operators ## \hat A, \hat A^\dagger ##, ## \hat x ## and ##\hat p ##. Homework Equations I know how to use all the above operators projecting them on...
  15. S

    B Conjugation , involving operators in Dirac Notation.

    In a PDF i was looking through i came about a question for the operator P = |a><b| find Px(adjoint) the adjoint was defined as <v|Px|u> = (<u|P|v>)* where u and v can be any bra and ket now for the question: (<u|a><b|v>)* = <v|Px|u> this is the confusing step , i thought conjugated simply...
  16. A

    Quantum state of system after measurement

    > Operator $$\hat{A}$$ has two normalized eigenstates $$\psi_1,\psi_2$$ with > eigenvalues $$\alpha_1,\alpha_2$$. Operator $$\hat{B}$$ has also two > normalized eigenstates $$\phi_1,\phi_2$$ with eigenvalues > $$\beta_1,\beta_2$$. Eigenstates satisfy: > $$\psi_1=(\phi_1+2\phi_2)/\sqrt{5}$$ >...
  17. S

    B Projection Operators: Explaining |m|2*|m|2 = |m|4

    Take a projection operatorPm=|m><m| However if the ket of m is a column matrix of m x 1 and its bra the complex conjugate with 1 x m length therefore <m|m> = |m|2 since the m here is the same since projection operator is the same. if A is a matrix B = A A*B=B*A but Pm*Pm = Pm (Projection...
  18. S

    MHB On the spectral radius of bounded linear operators

    Hi EVERYBODY: General knowledge: The homogeneous linear Fredholm integral equation $\mu\ \varPsi(x)=\int_{a}^{b} \,k(x,s) \varPsi(s) ds$ (1) has a nontrivial solution if and only if $\mu$ is an eigenvalue of the integral operator $K$. By multiplying (1) by $k(x,s)$ and...
  19. mjda

    I Ehrenfest Theorem: Enunciate & Implications for Classical/Quantum Mechanics

    This may seem rather silly, but how would I go about enunciating Ehrenfest’s theorem? Also, does anyone know what this theorem implies for the relation between classical and quantum mechanics? Any suggestions or help is greatly appreciated!
  20. binbagsss

    Hecke Operators and Eigenfunctions, Fourier coefficients

    Homework Statement Consider the action of ##T_2## acting on ##M_k(\Gamma_{0}(N)) ##, and show that ##\theta^4(n)+16F ## and ##F(t)## are both eigenfunctions. Functions are given by: Homework Equations For the Hecke Operators ##T_p## acting on ##M_k(\Gamma_{0}(N)) ##, the Hecke conguence...
  21. R

    Working with X and P operators in QM

    Homework Statement Consider the eigenstates of a particle in an infinite well with walls at ##x=\pm a##. without explicitly evaluating any integrals, what is the expectation value of the following operator $$\hat{x}^2\hat{p_x}^3+3\hat{x}\hat{p_x}^3\hat{x}+\hat{p_x}^3\hat{x}^2$$ Homework...
  22. F

    I Operators and vectors in infinite dimensional vector spaces

    Hello Everyone. I am searching for some clarity on this points. Thanks for your help: Based on Schrodinger wave mechanics formulation of quantum mechanics, the states of a system are represented by wavefunctions (normalizable or not) and operators (the observables) by instructions i.e...
  23. Robin04

    Differential operators in 2D curvilinear coordinates

    Homework Statement I’m studying orthogonal curvilinear coordinates and practice calculating differential operators. However, I’ve run across an exercise where the coordinate system is only in 2D and I’m confused about how to proceed with the calculations. Homework Equations A point in the...
  24. SemM

    A Understanding the Difference: Spectra of Unbounded vs. Bounded Operators

    Hi, why do unbounded operators and bounded operators differ so much in terms of defining their spectra? 1. The unbounded operator requires a self-adjoint extension to define its spectrum. 2. A bounded one does not require a self-adjoint extension to define the spectral properties. 3. Still the...
  25. F

    I What is the significance of commuting operators and CSCO in quantum mechanics?

    Hello, Today I am studying complete set of commuting observables (CSCO) which is a set of commuting operators, pair by pair, whose eigenvalues completely specify the state of a system. For example, given 4 different commuting observables, there is a set of eigenstates which are eigenstates for...
  26. SemM

    A Understanding Complex Operators: Rules, Boundedness, and Positivity

    Hi, from the books I have, it appears that some rules for operators, boundedness, positivity and possibly the definition of the spectrum regard real operators, and not complex operators. From the complex operator ##i\hbar d^3/dx^3 ## it appears that it can be defined as not bounded (unbounded)...
  27. C

    I Question about inverse operators differential operators

    Hi all, so I'm not sure if what I'm asking is trivial or interesting, but is there any general or canonical way to interpret say, The follwing operator? (Specifically in the study of quantum mechanics): A = 1/(d/dx) (I do not mean d-1/dx-1, which is the antiderivative operator ) How would...
  28. H

    B Question about Unitary Operators and symmetry

    We know that for every symmetry transformation, we can define a linear, unitary operator (or antiunitary, anti linear operator) that takes a physical state into another state. My question is if there exists unitary operators that act in this way that do not correspond to any symmetry? Would a...
  29. hideelo

    A Velocity dependence of operators in Inonu-Wigner contraction

    I'm reading Weinberg's QFT volume 1. At the end of section 2.4 he is deriving the Inonu-Wigner contraction where he reduces the Poincaré group to the Euclidean one by taking the low velocity limit. In analyzing how the operators depend on velocity there are some I understand and some I don't. I...
  30. SemM

    I How to find admissible functions for a domain?

    Hi, in a text provided by DrDu which I am still reading, it is given that "the momentum operator P is not self-adjoint even if its adjoint ##P^{\dagger}=-\hbar D## has the same formal expression, but it acts on a different space of functions." Regarding the two main operators, X and D, each has...
  31. Danny Boy

    A Defining Krauss operators with normal distribution

    I am interested in defining Krauss operators which allow you to define quantum measurements peaked at some basis state. To this end I am considering the Normal Distribution. Consider a finite set of basis states ##\{ |x \rangle\}_x## and a set of quantum measurement operators of the form $$A_C =...
  32. SemM

    A Does Commutativity Affect Linearity?

    Hi, I have in a previous thread discussed the case where: \begin{equation} TT' = T'T \end{equation} and someone, said that this was a case of non-linear operators. Evidently, they commute, so their commutator is zero and therefore they can be measured at the same time. What makes them however...
  33. SemM

    A The meaning of the commutator for two operators

    Hi, what is the true meaning and usefulness of the commutator in: \begin{equation} [T, T'] \ne 0 \end{equation} and how can it be used to solve a parent ODE? In a book on QM, the commutator of the two operators of the Schrödinger eqn, after factorization, is 1, and this commutation relation...
  34. SemM

    I Solving the Schrödinger eqn. by commutation of operators

    Hi, I noticed that the raising and lowering operators:\begin{equation} A =\frac{1}{\sqrt{2}}\big(y+\frac{d}{dy}\big) \end{equation}\begin{equation} A^{\dagger}=\frac{1}{\sqrt{2}}\big(y-\frac{d}{dy}\big) \end{equation}can be used to solve the eqn HY = EY However I am curious about something...
  35. S

    B Surjective/injective operators

    Hi, I found in Kreyszig that if for any ##x_1\ and\ x_2\ \in \mathscr{D}(T)## then an injective operator gives: ##x_1 \ne x_2 \rightarrow Tx_1 \ne Tx_2 ## and ##x_1 = x_2 \rightarrow Tx_1 = Tx_2 ##If one has an operator T, is there an inequality or equality one can deduce from this, in...
  36. P

    I Field operators and the uncertainty principle

    Hi, I am reading QFT by Lancaster and Blundell. In chapter 4 of the book the field operators are introduced: "Now, by making appropriate linear combinations of operators, specifically using Fourier sums, we can construct operators, called field operators, that create and annihilate particles...
  37. S

    A Are bounded operators bounded indepedently on the function?

    Hi thanks to George, I found the following criteria for boundedness: \begin{equation} \frac{||Bf(x)||}{||f(x)||} < ||Bf(x)|| \end{equation} If one takes f(x) = x, and consider B = (h/id/dx - g), where g is some constant, then B is bounded in the interval 0-##\pi##. However, given that I...
  38. Danny Boy

    A Quantum measurement operators with Poisson distribution

    The following is a somewhat mathematical question, but I am interested in using the idea to define a set of quantum measurement operators defined as described in the answer to this post. Question: The Poisson Distribution ##Pr(M|\lambda)## is given by $$Pr(M|\lambda) =...
  39. S

    A Is this operator bounded or unbounded?

    Hi, I have an operator which does not obey the following condition for boundedness: \begin{equation*} ||H\ x|| \leqslant c||x||\ \ \ \ \ \ \ \ c \in \mathscr{D} \end{equation*} where c is a real number in the Domain D of the operator H. However, this operator is also not really unbounded...
  40. J

    I Squaring a Sum of Ket-Bra Operators

    I can't follow the solution given in my textbook to the following problem. The solution goes right off the rails on the first step. Consider a system whose Hamiltonian is given by \hat H = \alpha \left( {\left. {\left| {{\phi _1}} \right.} \right\rangle \left\langle {\left. {{\phi _2}}...
  41. C

    A What are local and non-local operators in QM?

    In Hartree-Fock method, I saw the Fock operator has two integrals: Coulomb integral and exchange integral. One can define two operator. "The exchange operator is no local operator" why? Whats de diference: local and no local operator? And why do the operators have singularities? thanks
  42. M

    I Measurement Values for z-component of Angular Momentum

    Given a wave function $$\Psi(r,\theta,\phi)=f(r)\sin^2(\theta)(2\cos^2(\phi)-1-2i*\sin(\phi)\cos(\phi))$$ we are trying to find what a measurement of angular momentum of a particle in such wave function would yield. Attempts were made using the integral formula for the Expectation Value over a...
  43. M

    A Commutation and Non-Linear Operators

    Suppose ##A## is a linear operator ##V\to V## and ##\mathbf{x} \in V##. We define a non-linear operator ##\langle A \rangle## as $$\langle A \rangle\mathbf{x} := <\mathbf{x}, A\mathbf{x}>\mathbf{x}$$ Can we say ## \langle A \rangle A = A\langle A \rangle ##? What about ## \langle A \rangle B =...
  44. F

    I Bases, operators and eigenvectors

    Hello, In the case of 2D vector spaces, every vector member of the vector space can be expressed as a linear combination of two independent vectors which together form a basis. There are infinitely many possible and valid bases, each containing two independent vectors (not necessarily...
  45. Rodrigo Schmidt

    I Doubt about proof on self-adjoint operators.

    So the statement which the proof's about is: For every linear transformation ##A##(between finite dimension spaces), the product ##A^*A## is self-adjoint. So, the proof is: ##(A^*A)^*=A^*A^{**}=A^*A## What i don't understand is why ##(A^*A)^*=A^*A^{**}##. Isn't that true only if ##A## and...
  46. S

    I Maxwell's Equations, Hodge Operators & Tensor Analysis

    Hello! I am reading this paper and on page 18 it states that "in (2 + 1)D electrodynamics, p−form Maxwell equations in the Fourier domain Σ are written as: ##dE=i \omega B ##, ##dB=0##, ##dH=-i\omega D + J##, ##dD = Q## where H is a 0-form (magnetizing field), D (electric displacement field)...
  47. W

    I Hermitian Operators: Referencing Griffiths

    I have a few issues with understanding a section of Griffiths QM regarding Hermitian Operators and would greatly appreciate some help. It was first stated that, ##\langle Q \rangle = \int \Psi ^* \hat{Q} \Psi dx = \langle \Psi | \hat{Q} \Psi \rangle## and because expectation values are real...
  48. N

    Solving for <p>, <x> and <x^2> using raising and lowering operators

    Homework Statement A) Show that <x>=<p>=0 hint: use orthogonality B) Use the raising and lowering operators to evaluate an expression for < x2 > Homework Equations Also A- and A+ will definitely come in handy The Attempt at a Solution I tried setting up the equations for <x> and <p> but I...
  49. T

    I Can we operate with several operators at once on a state?

    It's known that the time-translation operator is ##\exp(-i Ht)## and the space-translation operator is ##\exp(i (p \cdot x))##. The former causes a time-translation for a state vector whereas the latter causes a space-translation. Can we operate with the two operators on the state vector? Like...
  50. 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...
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