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

    Projection operators and Weyl spinors

    I am working through some course notes where the aim is to derive the equations of motion satisfied by the left handed and right handed components of the Dirac spinor ##\psi##. From the Dirac lagrangian, we have $$\mathcal L = \bar \psi (i \not \partial P_L - m P_L)\psi_L + \bar \psi (i \not...
  2. S

    MHB Do Commuting Linear Integral Operators Share Eigenfunctions and Eigenvalues?

    I have two linear integral operators $Ky=\int_{a}^{b} \,k(x,s)y(s)ds$ $Ly=\int_{a}^{b} \,l(x,s)y(s)ds$ their kernels commute Do they have same eigenfunctions like matrices and for instance in this case their product is the product of their eigenvalues. I am poorly read in operator theory...
  3. I

    Hermitian adjoint operators (simple "proofs")

    Homework Statement I'm having some trouble with questions asking me to "show" or "prove" instead of computing an answer so I'm looking for some input if I'm actually doing what I'm supposed to or not (and for the last one I don't know where to get started really.) 1. Show that ##T^*## is...
  4. I

    Self adjoint operators, eigenfunctions & eigenvalues

    Homework Statement Consider the space ##P_n = \text{Span}\{ e^{ik\theta};k=0,\pm 1, \dots , \pm n\}##, with the hermitian ##L^2##-inner product ##\langle f,g\rangle = \int_{-\pi}^\pi f(\theta) \overline{g(\theta)}d\theta##. Define operators ##A,B,C,D## as ##A = \frac{d}{d\theta}, \; \; B=...
  5. S

    Ladder operators in Klein -Gordon canonical quantisation

    The quantum Klein-Gordon field ##\phi({\bf{x}})## and its momentum density ##\pi({\bf{x}})## are given in Fourier space by ##\phi({\bf{x}}) = \int \frac{d^{3}p}{(2\pi)^{3}} \frac{1}{\sqrt{2 \omega_{{\bf{p}}}}} \big( a_{{\bf{p}}} e^{i{\bf{p}} \cdot {\bf{x}}} + a^{\dagger}_{{\bf{p}}}...
  6. Elemental

    Spin Operators: Axial for QM, Polar in Clifford Algebra?

    Hello folks! New to this forum, so hoping I'm not retreading old ground. The Pauli matrices are spin angular momentum operators in quantum mechanics and thus are axial vectors. But in Clifford algebra in three dimensions they are odd basis elements and thus polar vectors. Hestenes, Baylis, other...
  7. ShayanJ

    Superselection rules and non-observable Hermitian operators

    Its usually said(like https://en.wikipedia.org/wiki/Superselectiond ) that superselection rules imply that not all Hermitian operators can be considered to be physical observables. But I don't understand how that follows. Can someone explain? Thanks
  8. A

    Operators implementation with operators

    Hello I may make some mistakes because I am not professional at physics:smile:.So I want to know how to implementate wave function with operators example:p(hat) impletated with ψ so: p(hat)ψ=pψ so as you saw it was momentum operator and momentum operator is:-iħ∂/∂x as you saw it is one...
  9. nmsurobert

    Operators and eigenstates/values

    Homework Statement Let the Hermitian operator A^ corresponding to the observable A have two eigenstates |a1> and |a2> with eigenvalues a1 and a2, respectively, where a1 ≠ a2. Show that A^ can be written in the form A^ = a1|a1><a1| + a2|a2><a2|. Homework EquationsThe Attempt at a Solution I...
  10. G

    How Fourier components of vector potential becomes operators

    Hello. I'm studying quantization of electromagnetic field (to see photon!) and on the way to reach harmonic oscillator Hamiltonian as a final stage, sudden transition that the Fourier components of vector potential A become quantum operators is observed. (See...
  11. maverick_76

    Questions about operators and commutators

    so I have an expression here: [P,g(r)]= -ih dg/dr P is the momentum operator working on a function g(r). Is this true because when you expand the left hand side the expression g(r)P is zero because the del operator has nothing to work on?
  12. Activeuser

    Ladder operators and matrix elements...

    Please I need your help in such problems.. in terms of ladder operators to simplify the calculation of matrix elements... calculate those i) <u+2|P2|u> ii) <u+1| X3|u> If u is different in both sides, then the value is 0? is it right it is 0 fir both i and ii? when exactly equals 0, please...
  13. ddd123

    Microcanonical partition function - Dirac delta of operators

    Homework Statement Why is it that the microcanonical partition function is ##W = Tr\{\delta(E - \hat{H})\}##? As in, for example, Mattis page 62? Moreover, what's the meaning of taking the Dirac delta of an operator like ##\hat{H}##? Homework Equations The density of states at fixed energy is...
  14. Vinay080

    How did physics operators come into being?

    Now I am starting to learn Quantum Mechanics. In the class I am taught about operators, postulates and all other basic stuff. I understand operators to be +, -, /, etc; but quantum mechanical operators are entirely different; to understand them, I think, I need to know the historical...
  15. V

    Linear Algebra - Linear Operators

    Homework Statement True or false? If T: ℙ8(ℝ) → ℙ8(ℝ) is defined by T(p) = p', so exists a basis of ℙ8(ℝ) such that the matrix of T in relation to this basis is inversible. Homework EquationsThe Attempt at a Solution So i think that my equations is of the form: A.x = x' hence A is...
  16. S

    Linear Operator L with Zero Matrix Elements

    Homework Statement Suppose a linear operator L satisfies <A|L|A> = 0 for every state A. Show that then all matrix elements <B|L|A> = 0, and hence L = 0. Homework Equations ##<A|L|A>=L_{AA} and <B|L|A>=L_{BA}## The Attempt at a Solution It seems very straight forward and I don't know how...
  17. M

    Operators in Quantum mechanics: can one swap \Psi and \Psi^*

    Homework Statement The demonstration for the momentum operator in Quantum Mechanics goes something like this <v>=\frac{d}{dt}<x>=\frac{d}{dt} \int x \Psi^* \Psi dx and then one ends up with <p>=m<v>=\int \Psi^* (-i \hbar \frac{d}{dx}) Psi dx however, if you swap the congugates you get...
  18. Logan Rudd

    Ladder operators to prove eigenstates of total angular momen

    Homework Statement Consider the following state constructed out of products of eigenstates of two individual angular momenta with ##j_1 = \frac{3}{2}## and ##j_2 = 1##: $$ \begin{equation*} \sqrt{\frac{3}{5}}|{\tiny\frac{3}{2}, -\frac{1}{2}}\rangle |{\tiny 1,-1}\rangle +...
  19. P

    Understanding the Conservation of Probability and Operators in Quantum Mechanics

    First, I have a question regarding the conservation of probability. The book shows (quite elegantly) that $$ \frac {d}{dt} \int_{-\infty}^{\infty} |\Psi (x, t)|^2dx = \frac {i\hbar}{2m} \Big{(}\Psi ^* \frac{\partial \Psi}{\partial x} - \frac{\partial \Psi ^*}{\partial x} \Big{)} \Big...
  20. D

    Interactions between field operators & locality in QFT

    Why is it required that interactions between fields must occur at single spacetime points in order for them to be local? For example, why must an interaction Lagrangian be of the form \mathcal{L}_{int}\sim (\phi(x))^{2} why can't one have a case where \mathcal{L}_{int}\sim\phi(x)\phi(y) where...
  21. W

    Commutation between operators of different Hilbert spaces

    Hi! If I have understood things correctly, in a multi-electron atom you have that the spin operator ##S## commutes with the orbital angular momentum operator ##L##. However, as these operators act on wavefunctions living in different Hilbert spaces, how is it possible to even calculate the...
  22. P

    Ladder operators for real scalar field

    Puting a minus in front of the momentum in the field expansion gives ##\phi \left( {\bf{x}} \right) = \int {{d^3}\tilde p} \left( {{a_{\bf{p}}}{e^{i{\bf{p}} \cdot {\bf{x}}}} + a_{\bf{p}}^ + {e^{ - i{\bf{p}} \cdot {\bf{x}}}}} \right){\rm{ }}\phi \left( {\bf{x}} \right) = \int {{d^3}\tilde...
  23. S

    Confusion regarding examples of Sturm-Liouville operators

    I have reading a paper where the functional determinants of differential operators are discussed: http://arxiv.org/abs/0711.1178 In the beginning of Section 3, the paper explains that functional determinants of operators of the form ##-\frac{d^{2}}{dx^{2}} + V(x)## can be found using a...
  24. S

    Commutator of creation/annihilation operators (continuum limit)

    Hi, This is a question regarding Example 3.6 in Section 3.5 (p.35) of 'QFT for the Gifted Amateur' by Lancaster & Blundell. Given, [a^{\dagger}_\textbf{p}, a_\textbf{p'}] = \delta^{(3)}(\textbf{p} - \textbf{p'}) . This I understand. The operators create/destroy particles in the momentum state...
  25. D

    Understanding Eigenfunctions and Operators in Quantum Mechanics

    Hello, so I have a couple of related questions. 1) If you have a wavefuction Ψ, and act on it with some operator, does it have to give you the same wavefunction back (ie. does the wavefunction have to be an eigenfunction of the operator)? Could you have a wavefunction like e-iħtSin(x)? Since...
  26. hideelo

    Deriving Commutation of Variation & Derivative Operators in EL Equation

    I am trying to do go over the derivations for the principle of least action, and there seems to be an implicit assumption that I can't seem to justify. For the simple case of particles it is the following equality δ(dq/dt) = d(δq)/dt Where q is some coordinate, and δf is the first variation in...
  27. C

    Product of two exponentials of different operators

    How does one show that eAeB=eA+Be[A,B]/2 where A,B are operators and [ , ] is the commutator. The QM book I am using states it as a fact without proof, but I would like to see how it is proved. I've muddled around with the series expansion, but can't get farther than a few term by term products...
  28. C

    Product of exponential of operators

    How does one show that eAeB=eA+Be[A,B]/2 where A,B are operators and [ , ] is the commutator. The QM book I am using states it as a fact without proof, but I would like to see how it is proved. I've muddled around with the series expansion, but can't get farther than a few term by term products...
  29. M

    Exploring Non-Linear Operators: An Intro to Derivatives

    Hello every one . If the derivative is a linear operator ( linear map ) Then what is the example of non-linear operator Thanks .
  30. Fantini

    MHB Relation between matrix elements of momentum and position operators

    Hello. I'm having trouble understanding what is required in the following problem: Find the relation between the matrix elements of the operators $\widehat{p}$ and $\widehat{x}$ in the base of eigenvectors of the Hamiltonian for one particle, that is, $$\widehat{H} = \frac{1}{2M} \widehat{p}^2...
  31. S

    Proving the adjoint nature of operators using Hermiticity

    How can the fact that ##\hat x## and ##\hat p## are Hermitian be used to prove that ##\hat x - \frac{i}{m \omega} \hat p## and ##\hat x + \frac{i}{m \omega} \hat p## are adjoints of each other?
  32. F

    Typing operators in PF threads

    Hi, I am new here. I don't know how can I type mathematical operators or symbols here. Can anyone help me out?
  33. _Kenny_

    Quantum conditions for position and momentum operators

    Hello! I'm currently making my way through the book "Quantum Field Theory of Point Particles and Strings" and on page 13 they talk are talking about quantization of the classical versions momentum and position. The first part to quantizing these is turning them into operators. The books goes on...
  34. hideelo

    Solving Notation & Convention Confusion in Differentials

    I am currently reading "Differential Equatons with Applications" by Ritger and Rose, and I need some clarification about some notation and convention that they are using. I think it all stems from a lack of clarity of the difference between the operator d/dx and the "object" (I don't know what...
  35. H

    Reps of the SUSY algebra: raising and lowering operators

    I'm reading Alvarez-Gaume review on Seiberg-Witten theory: http://arxiv.org/abs/hep-th/9701069. Around page 23 you can find the following claim: "This is a Clifford algebra with 2N generators and has a 2N-dimensional representation. From the point of view of the angular momentum algebra, a^I...
  36. A

    Operators change form for density matrix equations?

    Imagine applying an operator to a wave-function: \psi_t(x_1, x_2, ..., x_n) \rightarrow \frac{L_n(x)\psi_t(x_1, x_2, ..., x_n)}{||\psi_t(x_1, x_2, ..., x_n)||} Where ## \psi _t(x_1, x_2, ..., x_n) ## is initial system state vector, denominator is normalization factor, and Ln(x) is a...
  37. leafjerky

    Solve the system using differential operators.

    Homework Statement Solve the system using differential operators. Determine the # of arbitrary constants and then compare to your solution. Homework Equations D substitution: replace x' with Dx and y' with Dy The Attempt at a Solution I have the solution to this one, but I'm working...
  38. metapuff

    Do creation operators for different spins commute?

    Say I have a hamiltonian with fermion creation / annihilation operators like this: \sum_{k_1,k_2,k_3,k_4} c_{k_1,\uparrow}^{\dagger} c_{k_2,\downarrow}^{\dagger} c_{k_3,\downarrow} c_{k_4,\uparrow} where the k's are momenta and the arrows indicate spin up / spin down. Can I commute operators...
  39. A

    Proving Coherent States are Eigenfunctions of Annihilation Operators

    Look at the following attached picture, where they prove the coherent states are eigenfunctions of the annihiliation operators by simply proving aexp(φa†)l0> = φexp(φa†)l0>. I understand the proof but does that also prove that: aiexp(Σφiai†)l0> = φiexp(Σφiai†)l0> ? I can see that it would if you...
  40. P

    Help with Density Operators: Peter Yu Seeks Assistance

    I have difficulty in understanding the Density Operator. Please see attached file. (From the Book " Quantum Mechanics Demystified Page 250) Most grateful if someone could help! Peter Yu
  41. L

    Average values of operators of potential and kinetic energy

    In case of quantum LHO in eigen state of the system ##|n \rangle## \langle \hat{T} \rangle=\langle \hat{U} \rangle=\frac{1}{2}(n+\frac{1}{2})\hbar \omega What will happened in some superposition of states? Does Ehrenfest theorem can tell me something more general? Is it possible to say that...
  42. R

    Quantum Mechanics: Raising and Lowering Operators

    Homework Statement Consider a particle in an energy eigenstate ##|n\rangle.## Calculate ##\langle x\rangle## and ##\langle p_x\rangle## for this state. Homework Equations ##x = \sqrt{\frac{\hbar}{2m\omega}}(a+a^{\dagger})## The Attempt at a Solution ##\langle x\rangle =...
  43. T

    Creation and annihilation operators

    - a|n>=C|n-1> - a+|n>=D|n+1> And because |n-1> is normalized, <n-1|n-1>=1: (<n|a+)(a|n>)=C2 Thus, <n|a+a|n>=C2 Where a is the annihilation operator and a+ is the creation operator I don't understand this as...
  44. D

    Translation Operators: Raising & Lowering Equations

    α I have been studying translation operators of the type T = exp ( -ipx0/ hbar) where p is the momentum operator which leads to T+xT = x+x0. I am ok with that but then I came across the following equation concerning raising and lowering operators exp(-alpha a+) a exp(alpha a+) = a + alpha. Is...
  45. A

    Operators for comparing superposition components -- definable?

    Hello, I'm wondering, is it possible to define an operator on a Hilbert space that gives information about the "distinctness" of superposition components? As a simple example, imagine that we have two particles. Let |3> designate the state in which they are 3 meters apart, let |5> designate...
  46. A

    Operators for measuring superposition component distinctnes?

    Hello, I'm wondering, is it possible to define an operator that gives information about the "distinctness" of superposition components? As a simple example, imagine that we have two particles. Let |3> designate the state in which they are 3 meters apart, let |5> designate the state in which...
  47. blue_leaf77

    Does Commutativity Always Guarantee Shared Eigenkets?

    Let's denote ## \mathbf{p} ## and ## \Pi ## as the momentum and parity operators respectively. It's known that ## \mathbf{p} ## doesn't commute with ## \Pi ##, so they do not share the same set of eigenkets (plane wave doesn't have parity). But I just calculated that ##[\mathbf{p}^2,\Pi] = 0##...
  48. J

    Rotation operators on Bloch sphere

    Can anyone explain to me why the following operators are rotation operators: \begin{align*}R_x(\theta) &= e^{-i\theta X/2}=\cos(\frac{\theta}{2})I-i\sin(\frac{\theta}{2})X= \left(\!\begin{array}{cc}\cos(\frac{\theta}{2}) & -i\sin(\frac{\theta}{2}) \\ -i\sin(\frac{\theta}{2})&...
  49. D

    Expectation value of a combination of operators

    Homework Statement I will denote operators by capital letters. The question is calculate <p | XXPP | x> / <p | x > Homework Equations X |x> = x |x> P |p> = p |p> P |x> = -i(hbar)d/dx X |p> = i(hbar)d/dp The Attempt at a Solution If I start on the RHS and take PP out I get...
  50. L

    From observable to operators in QFT

    from the relativity forum https://www.physicsforums.com/threads/spacetime-in-qm-or-qft.802721/ Sonderval stated (transferred here so not off topic): http://scienceblogs.de/hier-wohnen-drachen/artikelserien/[/QUOTE'][/PLAIN] So the standard Schroedinger Equation can be used for both particles...
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