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. L

    Calculate sum. Fermionic operators

    Homework Statement How to calculate? ## \sum _{i,j} \langle 0|\prod_n \hat{C}_n \hat{C}^+_i\hat{C}_j \prod_n \hat{C}^+_n|0 \rangle ##Homework Equations ##\hat{C}^+, \hat{C}## are fermionic operators. ##\{\hat{C}_i,\hat{C}^+_j\}=\delta_{i,j}##The Attempt at a Solution I have a question. What is...
  2. nomadreid

    Yes/no question about non-commuting Hermitian operators

    Is the following a theorem? yes or no If A and B are non-commuting Hermitian operators (or matrices), there does not exist Hermitian operators C and D such that AB-BA = CD. (Or, as special case, ...there does not exist a Hermitian operator C s.t. C= AB-BA) Thanks
  3. R

    Find Adjoints of certain Operators

    Homework Statement Find the adjoints for x2d/dx and d2/dx2 Homework Equations I know that (x2)_dagger=x2 and that (d/dx)_dagger=-(d/dx). The Attempt at a Solution I solved x2d/dx by doing the following: (x2)_dagger * (d/dx)_dagger= (x2) * (-d/dx) thus the answer should be...
  4. Y

    Unitarity angular momentum operators

    Hi, I'm confused by a sentence in a set of lecture notes I have on quantum mechanics. In it, it is assumed there is some representation \pi of SO(3) on a Hilbert space. This representation is assumed to be irreducible and unitary. It is then said that the operators J_i, which are said to...
  5. C

    Commutators of Operators and Constants: A Quantum Mechanics Exercise

    Homework Statement Let ## \hat{A} = x ## and ## \hat{B} = \dfrac{\partial}{\partial x} ## be operators Let ## \hat{C} ## be defined ## \hat{C} = c ## with c some complex number. A commutator of two operators ## \hat{A} ## and ## \hat{B} ## is written ## [ \hat{A}, \hat{B} ] ## and is...
  6. S

    Is Squaring the Momentum Operator the Same as Applying it Twice?

    I'm, slowly, working through "Quantum Physics" by Stephen Gasiorowicz, second edition. On page 49, he gives the equation i\hbar\frac{\partial ψ(x, t)}{\partial t} = -\frac{\hbar^{2}}{2m}\frac{\partial ^{2}ψ(x, t)}{\partial x^2} He then makes the identification (h/i)(\partial/\partial x) =...
  7. tomwilliam2

    Operators on a Harmonic oscillator ground state

    Homework Statement Calculate the expectation value for a harmonic oscillator in the ground state when operated on by the operator: $$AAAA\dagger A\dagger - AA\dagger A A\dagger + A\dagger A A A\dagger)$$ Homework Equations $$AA\dagger - A\dagger A = 1$$ I also know that an unequal number of...
  8. Roodles01

    What are raising & lowering operators

    A little behind in this subject, but I understand raising & lowering operators to almost be factors of the Hamiltonian operator. raising - Ahat dagger = 1/√2 (x/a - a*(δ/δx)) lowering - Ahat = 1/√2 (x/a + a*(δ/δx)) I also have the Hamiltonian as; Hhat = (Ahat dagger * Ahat + 1/2)...
  9. W

    Eigenvalue problem with operators as matrix elements

    Hello, I have a feeling that the solution to this question is going to be incredibly obvious, so my apologies if this turns out to be really dumb. How do I solve the following eigenvalue problem: \begin{bmatrix} \partial_x^2 + \mu + u(x) & u(x)^2 \\ \bar{u(x)}^2 & \partial_x^2 + \mu +...
  10. P

    Eigenvalues, eigenvectors, eigenstates and operators

    Homework Statement Good evening :-) I have an exam on Wednesday and am working through some past papers. My uni doesn't give the model answers out, and I have come a bit stuck with one question. I have done part one, but not sure where to go from here, would be great if someone could...
  11. T

    Bilinear mappings, tensor products and p-summing operators

    Can somebody please explain bilinear maps, tensor products and p-summing operators in an easy-to-understand way. As though explaining to an undergraduate student who just knows basic linear algebra and basic functional analysis. And please give some nice examples to make the explanations more...
  12. mnb96

    Adjoint operators and diffeomorphism

    Hello, we known that for each linear operator \phi:\mathbb{R}^n\rightarrow \mathbb{R}^n there exists an adjoint operator \overline{\phi} such that: <\phi(\mathbf{x}),\mathbf{y}>=<\mathbf{x},\overline{\phi}(\mathbf{y})> for all x,y in ℝn, and where <\cdot,\cdot> is the inner product. My...
  13. U

    Derive all four propositional logic operators from nand

    So I recently learned that you can derive all four of the propositional logic operators (~, V, &, →) from Nand alone. As I have understood it, so long as you have negation, and one of the other operators, you can derive the rest. Like P → Q can be defined as ~P V Q. However, I learned that...
  14. M

    Operators and expectation values.

    I'm stuck on a question in atkins molecular quantum mechanics 4e (self test 1.9). If (Af)* = -Af, show that <A> = 0 for any real function f. I think you are expected to use the completeness relation sum,s { |s><s| = 1. I'm sure the answer is simple but I'm stumped.
  15. H

    Finding operators (and, possibly, exponents) in a system

    Hi, I have an algorithm that I have to test, and it gives me certain variables at different stages of time. I also have a "result" (I guess you can call it that), that these variables are supposed to amount to, in some mathematical fashion, at those equal points in time. This gives me a...
  16. J

    What do creation operators measure?

    My understanding is that in general, operators -- corresponding to observables -- act on a state (itself a member of an infinite-dimensional Hilbert space), and the eigenvalue is the value in that state (at least, if it's a pure state). To get an expectation value, you take the dot product of...
  17. M

    Properties of differential operators

    Homework Statement Hi, I am solving a system of differential equations and in one of my equations I have this, (D+2)X+(D+2)Y=0 where X and Y are variables, D is my differential operator. My question is, would it be mathematically correct to divide out (D+2) and thus getting X+Y=0, X=-Y ?
  18. T

    Proof of second quantization operators

    Please, can somebody show me why a Hamiltonian like \sum_nh(x_n) can be written as \sum_{i,j}t_{i,j}a^+_ia_j, with t_{i,j}=\int f^*_i(x)h(x)f_j(x)dx? Thank you.
  19. D

    Quantum Mechanical Operators - A Question Or Two

    A couple questions: is mass quantized? Energy is quantized, and momentum has eigenvalues for its operator so I took that to mean that momentum is also quantized. If those two are true (might not be! I'm new to this :tongue:), following E^2 = (pc)^2 + (mc^2)^2 Would that not mean that...
  20. D

    Can quantum operators be pictured in terms of wave packets?

    I've found the wave-packet picture quite useful as I work my way through the very basics of quantum mechanics. But I'm having trouble finding a wave-mechanical picture of operators. For example, at least in terms of a free particle, using the wave mechanics treatment (as opposed to the matrix...
  21. X

    Hermitian Conjugates and Operators

    Homework Statement Find the following hermitian conjugates and show if they are hermitian operators: i) xp ii) [x , p] iii) xp + px Where x is the position operator and p is the momentum operator. Homework Equations <f|Qg> = <Q^{t}f|g> Q = Q^{t} Hermitian operator p =...
  22. fluidistic

    Adjoint of linear operators

    Homework Statement I must show several properties about linear operators using the definition of the adjoint operator. A and B are linear operator and ##\alpha## is a complex number. The first relation I must show is ##(\alpha A + B)^*=\overline \alpha A^*+B^*##. Homework Equations The...
  23. B

    Eigenvalues of unitary operators

    Homework Statement We only briefly mentioned this in class and now its on our problem set... Show that all eigenvalues i of a Unitary operator are pure phases. Suppose M is a Hermitian operator. Show that e^iM is a Unitary operator. Homework Equations The Attempt at a Solution...
  24. T

    Operators and the position representation

    I have a question about the formalism of quantum mechanics. For some operator A... \langle x |A|\psi\rangle = A\langle x | \psi \rangle Can this be derived by sticking identity operators in or is it more a definition/postulate. Thanks.
  25. L

    Creation and annihilation operators

    In one dimensional problems in QM only in case of the potential ##V(x)=\frac{m\omega^2x^2}{2}## creation and annihilation operator is defined. Why? Why we couldn't define same similar operators in cases of other potentials?
  26. L

    Time evolution of operators as projectors - confusion

    I have a confusion regarding expressing operators as projectors in Schrodinger and Heisenberg pictures. Please help. Consider a two-state system with |1> and |2> We know that e.g. a raising operator can be expressed as: \hat{\sigma}_+=|2><1| But here's my line of thought: In the...
  27. Ackbach

    MHB Probability and Operators in Quantum Mechanics

    Unfortunately, I can't find the thread (if someone finds it, please let me know, and I'll merge this post onto that thread), but someone asked why it is that in quantum mechanics, if you have an observable $B$, that the expectation value (average value) $\langle B \rangle$ is given by $$\langle...
  28. P

    Continuity equation, partial derivative and differential operators

    Hi all! I have the following slide, and whilst I understand that the original point is "the rate of density, ρ, in each volume element is equal to the mass flux"...i am totally lost on the mathematics! (And I am meant to be teaching this tomorrow). I do not have any information on what the...
  29. J

    Contracting operators in Wick diagrams

    Hi, I'm currently going through Ticciati's book along with the notes from Sidney Coleman's course and I have a question pertaining to Wick diagrams/expansion of S. In their example (section 4.3 of Ticciati and lecture 9 in Coleman's notes) they never seem to contract the adjoint nucleon field...
  30. P

    Quick question about raising and lowering operators (ladder operators)

    Reading through my QM text, I came across this short piece on ladder operators that is giving me trouble (see picture). What I am struggling with is how to get to equations 2 and 3 from equation 1. Can someone point me in the right direction? Where does the i infront of the x go?
  31. B

    Confirmation concept questions eigenfunctions and operators

    Homework Statement Are the momentum eigenfunctions also eigenfunctions of e free particle energy. Operator? Are momentum eigenfunctions also eigenfunctions of the harmonic oscillator energy operator? An misplayed system evolves with time according to the shrodinger equation with potential...
  32. D

    Finding the Commutator of Two Operators

    Homework Statement Hello. I am supposed to find the commutator between to operators, but I can't seem to make it add up. The operators are given by: \hat{A}=\alpha \left( {{{\hat{a}}}_{+}}+{{{\hat{a}}}_{-}} \right) and \hat{B}=i\beta \left( \hat{a}_{+}^{2}-\hat{a}_{-}^{2} \right), where alpha...
  33. Z

    Nonlinear Operators on Finitely Generated Vector Spaces: Group Property Example

    Can someone give an example of a nonlinear operator on a finitely generated vector space(preferably ℝn)? I'd be particularly interested to see an example of such that has the group property as well.
  34. P

    Time derivative of creation/annhilation operators

    Basically is it possible to take a time derivative of a creation/annhilation operator?
  35. E

    A question on the product of two real linear operators

    I am reading The Principles of Quantum Mechanics 4th Ed by Paul Dirac, specifically where he introduces his own Bra-Ket notation. You can view this book as a google book. http://books.google.com.au/books?id=XehUpGiM6FIC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false...
  36. M

    Is A=5 and A=x Linear Operators?

    Linear operator A is defined as A(C_1f(x)+C_2g(x))=C_1Af(x)+C_2Ag(x) Question. Is A=5 a linear operator? I know that this is just number but it satisfy relation 5(C_1f(x)+C_2g(x))=C_15f(x)+C_25g(x) but it is also scalar. Is function ##A=x## linear operator? It also satisfy...
  37. D

    Proof that all operators are linear

    "Proof" that all operators are linear I've "proven" that all operators acting on a Hilbert space are linear. Obviously this isn't true, so there must be a fault in my reasoning somewhere. I having trouble finding it though, and would appreciate input by someone who can. Let |\psi\rangle =...
  38. Demon117

    Do angular momentum operators anti-commute?

    I know that L and S commute, but does this mean they do not anticommute? [L,S]=0. \left\{L,S\right\}=0?
  39. DrClaude

    Separating operators into classical + quantum

    In the paper http://link.aps.org/doi/10.1103/PhysRevA.85.062329, the authors separate the position and momentum operators into classical motion and quantum fluctuations: \hat{X}_i \equiv \bar{X}_i + \hat{q}_i; \quad \hat{P}_i \equiv \bar{P}_i + \hat{\pi}_i Can someone point me to a reference...
  40. J

    Lorentz action on creation/annihilation operators

    Hi, I'm currently reading the book "Quantum Field Theory for Mathematicians" by Ticciati and in section 2.3 he mentions that the Lorentz action on the free scalar field creation operators \alpha(k)^\dagger is given by U(\Lambda)\alpha(k)^\dagger U(\Lambda)^\dagger = \alpha(\Lambda...
  41. R

    Why Do We Need Fields as Annihilation & Creation Operators?

    Can anyone tell me why it is necessary to express a field as annhilation and creation operators? I just don't see why we need a field to explain the creation of particles in relativity, after all two colliding particles with enough energy produce some more.
  42. Roodles01

    What is the role of linear operators in quantum mechanics?

    Homework Statement Just starting third level Uni. stuff & am faced with linear operators from Quantum Mechanics & need a little help. OK, an operator, Ô, is said to be linear if it satisfies the equation Ô(α f1 + β f2) = α(Ô f1) + β(Ô f2) Fine but I have an equation I can't wrap my...
  43. micromass

    Are there any physical implications of working with unbounded operators in QM?

    It is well known that unbounded operators play a crucial role in the mathematical formulation of quantum mechanics. In some sense, unbounded operators are inevitable. Indeed, we can prove that if A and B are self-adjoint operators such that [A,B]=ih, then A and B can never both be bounded. My...
  44. A

    Finding Matrix Elements of Operators in Quantum Mechanics

    If you have an operator a represented in some basis l1>, l2> you find its matrix elements by doing Aij = <ilAlj> But more oftenly you are interested in the expectation value of A. So you take: <ψlAlψ>. My teacher tends to call these numbers matrix elements too. But which matrix element...
  45. S

    How exactly do raising/lowering operators let you know the form of M?

    There must be some lapse in my understanding of this. I understand that you can have an eigenstate of a system with an angular momentum magnitude value and a value for one component of the angular momentum (z). Using the lowering and raising operators we can create states (or deduce that states...
  46. A

    Expectation values of spin operators in changing magnetic field

    Homework Statement Homework Equations The Attempt at a Solution I have totally no idea how to solve this question. But I find it somehow similar to the Larmor precession problem. Therefore I try to solve my problem by referring to that. Are there any mistakes if I do it like...
  47. T

    Regarding mathematical operators

    One basic operator is addition. In order to add the any number x number of times, multiplication was invented. In order to multiply any number x number of times, exponentiation was invented. What if we want to raise a number to a power x number of times? How come we didn't invent that? Also...
  48. ShayanJ

    Equality of Operators A & B on Hilbert Space H

    Imagine we have two operators A and B on a complex hilbert space H such that: [A,B] \psi = (AB-BA) \psi=c \psi \ \ \ \ \psi \epsilon H \mbox{ and } c \epsilon C Then can we say that [A,B] is the same as cI when I is the identity operator?Why? Thanks
  49. J

    Manipulation of partial differential operators.

    Homework Statement Given that u(x,y) and y(x,z) are both continuous, differentiable functions show that (\frac{\partial u}{\partial z})x=(\frac{\partial u}{\partial y})x(\frac{\partial y}{\partial z})x Homework Equations Only equations given above The Attempt at a Solution I...
  50. ShayanJ

    Canonically conjugate operators

    I've searched for this but found nothing,so I ask it here. What are canonically conjugate operators? Is [A,B]=cI a definition for A and B being canonically conjugate? Thanks
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