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. Fredrik

    Frequency Operators & Ensemble Measurements

    The fraction of members of a set of numbers \{k_i\}_{i=1}^N that are equal to a specific number k can be written as \frac 1 N\sum_{i=1}^N\delta_{kk_i} Now consider an ensemble of N identical systems. Because of the above, the operator f_k^{(N)} defined by...
  2. L

    Eigenvalues of linear operators

    Let V be the vector space of all real integrable functions on [0,1] with inner product <f,g>=\int_0^1 f(t)g(t)dt Three linear operators defined on this space are A=d/dt and B=t and C=1 so that Af=df/dt and Bf=tf and Cf=f I need to find the eigenvalues of these operators: For A...
  3. M

    Commutation of angular momentum operators

    Homework Statement None of the operators Lz, Ly and Lx commute. Show that [Lx,Ly] = i(h-cross)Lz Homework Equations Where Lx is defined as Lx=-ih ( y delta/delta x - z delta/delta y) Where Ly is defined as Ly=-ih ( z delta/delta x - x delta/delta z) Where Lz is defined as Lz=-ih (...
  4. P

    Very Basic QM problem: Commuter of position and momentum operators

    I'm not exactly sure if this belongs in introductory or advanced physics help. Homework Statement In my book, the author was explaining the proof of the Uncertainty relation between po position and momentum. It simply stated that [x,p]= ih(h is reduced) But when I tried to verify it I got...
  5. K

    Exploring NMR Operators: I_x, I_y, I_z

    I'm reading a paper on NMR, and the authors keep referring to the operators I_x, I_y, I_z . What are these operators? I keep finding them mentioned in other papers, but no description of what they are.
  6. Pengwuino

    Degenerate basis, incomplete set of operators

    I may have heard this or understood this incorrectly, so if i am asking the wrong question, feel free to correct me. As I understand it, if you have a degenerate set of simultaneous eigenvectors, you haven't specified a complete set of operators. For example, the hydrogen atom. You typically...
  7. Fredrik

    Unbounded operators in non-relativistic QM of one spin-0 particle

    What exactly are the axioms of non-relativistic QM of one spin-0 particle? The mathematical model we're working with is the Hilbert space L^2(\mathbb R^3) (at least in one formulation of the theory). But then what? Do we postulate that observables are represented by self-adjoint operators? Do we...
  8. K

    Hermitian Operators: Homework Equations & Attempt at a Solution

    Homework Statement Homework Equations The Attempt at a Solution I've gone round in circles doing this! I started of by writing it as an integral of (psi* x A_hat2 x psi) w.r.t dx, then using the equation above but I keep coming back at my original equation after flipping it...
  9. B

    Ladder operators in quantum mechanics

    Homework Statement This is problem 2.11 from Griffith's QM textbook under the harmonic oscillator section. Show that the lowering operator cannot generate a state of infinite norm, ie, \int | a_{-} \psi |^2 < \infty Homework Equations This isn't so hard, except that I consistently get the...
  10. M

    CFG to CNF - unary/associative operators

    Homework Statement I'm trying to convert a context free grammar into Chomsky's normal form. These are the productions of my grammar: S -> 0|1|a|b|S+S|S.S|S*|(S) Where 0, 1, a, b are terminals, +, . are binary operators and *,() are unary operators. I know that for a grammar to be in CNF...
  11. L

    How Are Angular Momentum Operators Calculated in Spherical Polar Coordinates?

    How does one obtain the formulae for the angular momentum operators in spherical polar coordinates i.e. \hat{L_x}=i \hbar (\sin{\phi} \frac{\partial}{\partial{\theta}} + \cot{\theta} \cos{\phi} \frac{\partial}{\partial{\phi}} \hat{L_y}=i \hbar (-\cos{\phi}{\phi}...
  12. P

    Understanding Hilbert-Schmidt Operators: Eigenvectors and Symmetry

    Homework Statement Let K be a Hilbert-Schmidt kernel which is real and symmetric. Then, as we saw, the operator T whose kernel is K is compact and symmetric. Let \varphi_k(x) be the eigenvectors (with eigenvalues \lambda_k) that diagonalize T . Then: a. K(x,y) \sim \sum_k \lambda_k...
  13. V

    Lz and L^2 are commuting operators

    Homework Statement Using the definitions of Lz and L^2, show that these two operators commute. Homework Equations Lz = -ih_bar * d/d(phi) L^2 = -(h_bar)^2 {1/sin(theta) * d/d(theta) * [sin(theta) * d/d(theta)] + 1/sin^2(theta) d^2/d(phi)^2} The Attempt at a Solution I'm actually...
  14. S

    Finding Observable Values from Hermitian Measurement Operators

    Homework Statement OK, so assuming we have a physical observable with three values, a(1),a(2) and a(3), and there are given matrices for the measurement operators M(a(1))...M(a(3)). How does one actually go about finding a(1),a(2) and a(3) given the matrices?The Attempt at a Solution These...
  15. J

    Scaling dimensions of operators in AdS/CFT

    I have a question about Witten's original 1998 paper on AdS/CFT http://arxiv.org/abs/hep-th/9802150 Since the AdS metric diverges at the boundary, the boundary metric is only defined up to a conformal class Eq. (2.2), ds^2 \to d\widetilde{s}^2 = f^2 ds^2 Similarly, the solution for...
  16. J

    Dirac-Feynman-action principle and pseudo-differential operators

    I have encountered some mathematical difficulties when examining a one dimensional system defined by a Lagrange's function L(x,\dot{x}) = M|\dot{x}|^{\alpha} - V(x), where \alpha > 1 is some constant. The value \alpha=2 is the most common, but I am now interested in a more general...
  17. F

    Hermitian Operators and Eigenvalues

    Homework Statement C is an operator that changes a function to its complex conjugate a) Determine whether C is hermitian or not b) Find the eigenvalues of C c) Determine if eigenfunctions form a complete set and have orthogonality. d) Why is the expected value of a squared hermitian...
  18. N

    QM: Arbitrary operators and their eigenstates

    Homework Statement Hi all. When riding home today from school on my bike, I was thinking about some QM. The general solution to the Schrödinger equation for t=0 is given by: \Psi(x,0)=\sum_n c_n\psi_n(x), where \psi_n(x) are the eigenfunctions of the Hamiltonian. We know that the...
  19. S

    Matrix representing projection operators

    Hey everyone! I have a question regarding the matrix representation of a projection operator. Specifically, does the wavefunction have to be normalized before determining the projection operator? For example: |Ψ1> = 1/3|u1> + i/3|u2> + 1/3|u3> |Ψ2> = 1/3|u1> + i/3|u3> Ψ1 is obviously...
  20. O

    Virasoro operators in bosonic String Theory

    In a recent lecture on String Theory, we encountered the divergent sum 1+2+3+... when calculating the zero mode Virasoro operator in bosonic String Theory. This divergent sum is then set equal to a finite negative constant - the argument for doing so was a comparison with the definition of the...
  21. G

    What are the operations on vector field A and how do I simplify the results?

    Hello. I am stuck trying to find an understandable answer to this online: Carry out the following operations on the vector field A reducing the results to their simplest forms: a. (d/dx i + d/dy j + d/dz k) . (Ax i + Ay j + Ax k) b. (d/dx i + d/dy j + d/dz k) x (Ax i + Ay j + Ax k) I...
  22. Fredrik

    Construction of a Hilbert space and operators on it

    When quantizing a classical field theory, e.g. Klein-Gordon theory, the Hilbert space of one-particle states is taken to be a set of equivalence classes of (Lebesgue) measurable and square integrable solutions of the classical field equation, but how do you use the classical theory to construct...
  23. maverick280857

    What is the generalization of the BAC-CAB rule for operators?

    Hi Short question: What is the generalization of the BAC-CAB rule for operators? Longer question and context: please read below I was reading Schiff's book on Quantum Mechanics (3rd Edition) and on page 236, he has defined a generalized Runge-Lunz vector for a central force as \vec{M} =...
  24. S

    Raising and Lowering momentum operators

    I tried to use the eigenvalue of the operators but I couldn't get the result. Can anyone help me to understand this relationship? Thank you.
  25. M

    Treating operators with continuous spectra as if they had actual eigenvectors?

    I'm trying to teach myself quantum mechanics from Dirac, and I'm having trouble justifying some of the maths, in particular how we can just jump out of the confines of a Hilbert space when it's convenient. Dirac rather liberally talks about observables that have a continuous range of...
  26. P

    Raising and lowering operators acting on spin 1 kets?

    I read in my notes that S{-}|1> = sqrt(2)h(bar)|0> and similar for all six products of using the raising and lowering operators on |1>, |0>, |-1> I don't understand where the sqrt(2)h(bar) has come from? Cheers Philip
  27. D

    Sakurai 1.27 - Transformation Operators

    Problem Suppose that f(A) is a function of a Hermitian operator A with the property A|a'\rangle = a'|a'\rangle. Evaluate \langle b''|f(A)|b'\rangle when the transformation matrix from the a' basis to the b' basis is known.The attempt at a solution Here's what I have... I'm not sure if the last...
  28. D

    Sakurai 1.17 - Operators and Complete Eigenkets

    I'm pretty sure this is correct, but could someone verify for rigor? Problem Two observables A_1 and A_2, which do not involve time explicitly, are known not to commute, yet we also know that A_1 and A_2 both commute with the Hamiltonian. Prove that the energy eigenstates are, in general...
  29. S

    Normal, self-adjoint and positive definite operators

    I have two questions: 1. Let V be a finite dimensional inner product space. Show that if U: V--->V is self-adjoint and T: V---->V is positive definite, then UT and TU are diagonalizable operators with only real eigenvalues. 2. Suppose T and U are normal operators on a finite dimensional...
  30. diegzumillo

    Limited operators - continuity?

    Hi there! :) I'm trying to understand a theorem, but it's full with analysis (or something) terms unfamiliar to me. Is there an intuitive interpretation for the sentence: 'An operator being limited is equivalent to continuity in the topolgy of the norm'? Also, how can I partially...
  31. P

    Raising and lowering operators on a ket?

    How do you use the S(+) and S(-) operators on integer kets, |1>, |-1>, |0>? I'm told the outcome of the ones which aren't zero will be something like h(bar)/sqrt(2) * |ket> Confused!? I thought operators are 2 x 2 matrices... Any help much appreciated, Philip
  32. D

    Explore Banach Spaces and Bounded Linear Operators

    Homework Statement http://img252.imageshack.us/img252/4844/56494936eo0.png 2. relevant equations BL = bounded linear space (or all operators which are bounded). The Attempt at a Solution I got for the first part: ||A||_{BL} =||tf(t)||_{\infty} \leq ||f||_{\infty} so ||A||_{BL} \leq 1...
  33. E

    Commutate relation of lowering operator and sperical tensor operators

    Hi all, I found a commutation relation of lowering operator(J-) and spherical operator in Shankar's QM (2ed, page 418, Eq 15.3.11): [J_-,T_k^q] = - \hbar \sqrt{(k+q)(k-q+1)} T_k^{q-1} I wonder how the minus sign in the beginning of the right hand side come out? I have googled some...
  34. P

    Commutation of 2 operators using braket notation?

    How do you work out the commutator of two operators, A and B, which have been written in bra - ket notation? alpha = a beta = b A = 2|a><a| + |a><b| + 3|b><a| B = |a><a| + 3|a><b| + 5|b><a| - 2|b><b| The answer is a 4x4 matrix according to my lecturer... Any help much appreciated...
  35. diegzumillo

    Show that Isospin operators satisfy the SU(2) algebra

    Hi there! Doesn't seem like a hard problem.. Homework Statement Show that the 3 isospin operators, defined by T_{+}\left\vert p\right\rangle =0, T_{-}\left\vert n\right\rangle =0, T_{+}\left\vert n\right\rangle =\left\vert p\right\rangle, T_{-}\left\vert p\right\rangle =\left\vert...
  36. A

    Operators having Hermitian/Antihermitian part?

    Someone told me that any operator can be decomposed in a Hermitian and Antihermitian part. Is this true? How? By addition?
  37. B

    1d potential and switching between operators

    Homework Statement Homework Equations The Attempt at a Solution As a group we're stuck on this as a result of the lecturer saying that he wouldn't help us because we should work as a group and find other ways other than asking him about it. Which is fair enough - but none of us...
  38. N

    Hermitian Operators and the Commutator

    Homework Statement If A is a Hermitian operator, and [A,B]=0, must B necessarily be Hermitian as well? Homework Equations The Attempt at a Solution
  39. A

    Question about electric fields and operators

    Homework Statement I have three questions concerning the electric field: 1- When calculating an electric flux for a spherical charge distribution my proffessor always writes "4 pi r2 E(r) = flux", where E(r) is the electric field. I don't understand this. I've tried to calculate the...
  40. N

    Operators: Do they carry units?

    Homework Statement Hi all. The title says it all: Say we have an operator - e.g. the Hamiltonian. Does this have units? I.e. does the Hamiltonian have units of Joules or nothing? Personally I think it is nothing, since it is an operator, but I need confirmation.
  41. A

    Exploring the Use of Separable Metric Spaces in Random Operators

    operators are those functions which are having domain any set or any function the range is also a function. In simple words operators is a machine which is having domain and range as a set of functions. random operators are those spectiol type of fuctions which are define on a measured space.
  42. J

    Spectral theorem for discontinuous operators

    Hi all, I'm trying to extract a complete set of states, by applying the spectral theorem to the following differential operator: L = -\frac{d^2}{dx^2} + \mathrm{rect}(x) where rect(x) is the (discontinuous) rectangular function: http://en.wikipedia.org/wiki/Rectangular_function I...
  43. S

    ^, the operators in quantum mecħanics

    The doubt: It's not a problem, but a doubt. We know that in general quantum physics at undergraduate level, we write pΨ = (ħ/i) dΨ/dx. My doubt is that if we derived this equation from Schrodinger's equation only, so we must operate p on a wave-function only, which satisfies Schrodinger's...
  44. R

    Commuting creation and annihilation operators

    Hello, I have the missfortune of having to calculate a commutator with some powers of the creation and the annihilation operators, something like: \left[ a^m , (a^{\dagger})^n \right] I have managed to derive \left[ a^m , (a^{\dagger})^n \right]= m a^{m-1} \left[ a , a^{\dagger}...
  45. J

    Invariant subspaces under linear operators

    Homework Statement Prove or give a counterexample: If U is a subspace of V that is invariant under every operator on V, then U = {0} or U = V.Homework Equations U is invariant under a linear operator T if u in U implies T(u) is in U.The Attempt at a Solution Assume {0} does not equal U does not...
  46. H

    Hermitian vs. self-adjoint operators

    Hello, what's the difference between Hermitian and self-adjoint operators? Our professor in Group Theory made a comment once that the two are very similar, but with a subtle distinction (which, of course, he failed to mention :smile: ) Thanks!
  47. W

    Linear operators and a change of basis

    So...I've got an operator. Omega = (i*h-bar)/sqrt(2)[ |2><1| + |3><2| - |1><2| - |2><3| ] Part a asks if this is Hermitian, and my answer, unless I'm missing something, is no. Because the second part in square brackets is |1><2| + |2><3| - |2><1| - |2><3| which is not the same as Omega...
  48. A

    Calculating Spin Operators for Spin 1/2 Systems

    1. 1) Consider a spin 1/2 system... a) write expressions for the operators Sx Sy Sz in the basis composed of eigenkets of Sz b) Write eigenvalues of Sx Sy Sz c) Write eigenvectors of Sx and Sy in this basis 2) Write a matric corresponding to the operator S_ in the basis composed of the...
  49. J

    Densely defined operators of Fock space

    Could someone prove the following (if it is precisely correct): Since Fock space is the closure of the finite linear span of finite excitations of the vacuum state $\Omega$, then the operator $\hat{O}$ is densely defined if and only if $\hat{O} \Omega$ has finite norm. Or more...
  50. M

    What Are Differential Operators and Their Applications?

    Hi all! I came upon an expression like that: ' \frac{\delta f(x)}{\delta x} ' several times but can't figure out what it's used for. In Wikipedia it's posted that this derivative type is used when we consider infinitesimally small argument 'x'. So, does this mean: \frac{\delta...
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