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

    Need help with commute problem with operators

    Hi All, I just found this site and this is my first post here. I am working on getting my masters in polymer chemistry and started taking a class this semester which is pretty much all calculus and linear algebra and I just have a hard time with these subjects. I got a homework problem that I...
  2. T

    Evaluating annihilation and creation operators

    1. Evaluate the following (i.e. get rid of the operators)...
  3. A

    Rules for transforming operators

    The attached picture shows a representation of a general operator, which I found quite weird. The matrix elements are calculated in the position basis as far as I can tell, but I am not sure how. Do they do something like? <klTlk'> = ∫ dx dx' <klx><xlTlx'><x'lk'> In that case what happens to...
  4. A

    Why Do Fermion and Boson Operators Commute?

    For bosons we define states as eg. ln> = l1 0 1 ... > where the numbers denote how many particles belong to the j'th orbital. And similarly for fermions. We then define creation and anihillation operators which raise and lower the number of particles in the j'th orbital: c_j...
  5. G

    Commutator of exponential operators

    How do I compute the commutator [a,e^{-iHt}], knowing that [H,a]=-Ea? I tried by Taylor expanding the exponential, but I get -iEta to first order, which seems wrong.
  6. A

    How Do Delta Functions Simplify the Fourier Transform in Quantum Mechanics?

    Homework Statement The exercise is a) in the attached trial. I have attached my attempt at a solution, but there are some issues. First of all: Isn't the example result wrong? As I demonstrate you get a delta function which yields the sum I have written (as far as I can see), not the sum...
  7. C

    New irrational number to develop transcendental operators

    Other than Bernouilli, Euler, and Lagrange, who else discovered an irrational number in which transcendental operators have been developed to simplify physics and geometry?
  8. S

    How to understand operators representing observables are Hermitian?

    As we know, all operators representing observables are Hermitian. In my undersatanding, this statement means that all operators representing observables are Hermitian if the system can be described by a wavefunction or a vector in L2. For example, the momentum operator p is Herminitian...
  9. A

    Are resolvents for self-adjoint operators themselves self-adjoint?

    Let T be a (possibly unbounded) self-adjoint operator on a Hilbert space \mathscr H with domain D(T), and let \lambda \in \rho(T). Then we know that (T-\lambda I)^{-1} exists as a bounded operator from \mathscr H to D(T). Question: do we also know that (T-\lambda I)^{-1} is self-adjoint? Can...
  10. F

    Spherical harmonics and angular momentum operators

    When solving for the spherical harmonic equations of the orbital angular momentum this textbook I'm reading.. Does this mean that there must be a max value of Lz which is denoted by |ll>? Normally the ket would look like |lm>, and since m is maxed at m=l then |ll> is the ket consisting of the...
  11. T

    A simple equality of Generalized Lorentz Operators

    Homework Statement Hi we have Lorentz operators J^{\mu\nu} = i(x^{\mu}\partial^{\nu} - x^{\nu}\partial^{\mu}) and these have [J^{\mu\nu}, J^{\rho\sigma}] = i(\eta^{\nu\rho}J^{\mu\sigma} + \eta^{\mu\sigma}J^{\nu\rho} - \eta^{\mu\rho}J^{\nu\sigma} - \eta^{\nu\sigma}J^{\mu\rho}) Now define...
  12. A

    What is the significance of commutative operators in quantum mechanics?

    What do we mean by the two operators are commutative or non commutative? I wanted to understand the physical significance of the commutative property of the operators. We are doing the introduction to quantum mechanics and there are many things that are really confusing. Any help will be...
  13. G

    Are functionals and operators the same thing?

    Are functionals a special case of operators (as written on Wiki)? Operators are mappings between two vector spaces, whilst a functional is a map from a vector space (the space of functions, say) to a field [or from a module to a ring, I guess]. Now, the field is NOT NECESSARILY a vector...
  14. H

    Showing determinant of product is product of dets for linear operators

    Homework Statement Assume A and B are normal linear operators [A,A^{t}]=0 (where A^t is the adjoint) show that det AB = detAdetB Homework Equations The Attempt at a Solution Well I know that since the operators commute with their adjoint the eigenbases form orthonormal sets...
  15. D

    Understanding Probability Amplitude, State Operators and Galilei Group

    Greetings, Just checking if I'm getting this ... please correct me if I'm wrong. The value of the wavefunction is 'probability amplitude' in discrete case and 'probability amplitude density' in continuous case. The former is a dimensionless complex number and the latter is the same...
  16. I

    Quantum, Spin, Orbital Angular momentum, operators

    Homework Statement If a particle has spin 1/2 and is in a state with orbital angular momentum L, there are two basis states with total z-component of angular momentum m*hbar l L,s,Lz,sz > which can be expressed in terms of the individual states ( l L,s,Lz,sz > = l L,Lz > l s,sz > ) as l...
  17. A

    Creation and anihillation operators

    The fundamental idea of these operators is that we can use them to add particles to our system to a specific eigenstate. Now my book has examples of these operators of which the harmonic oscillator ladder operators are used. But thinking about it, this example does not make sense for me. The...
  18. T

    MHB Prove the following; (vector spaces and linear operators)

    a) V = U_1 ⊕ U_-1 where U_λ = {v in V | T(v) = λv} b) if V = M_nn(R) and T(A) = A^t then what are U_1 and U_-1 When V is a vector space over R, and T : V -> V is a linear operator for which T^2 = IV .
  19. lonewolf219

    Operators with commutator ihbar

    I know that the commutator of the position and momentum operators is ihbar. Can any other combination of two different operators produce this same result, or is it unique to position and momentum only?
  20. A

    Representing Operators as Matrices and Differential Operators

    An operator A defined by a matrix can be written as something like: A = Ʃi,jlei><ejl <eilAlej> How does this representation translate to a continuous basis, e.g. position basis, where operators are not matrices but rather differential operators etc. Can we still write for e.g. the kinetic...
  21. K

    Do Hamiltonians Fully Represent All Observables in Quantum Mechanics?

    It is said that each observable like position or momentum is represented by a Hermitian operator acting on the state space. And the Hamiltonian is the total energy of the system, kinetic and potential.. so it means the Hamiltonians encode or encompass the energy of all observables (like...
  22. D

    Which Operators Commute in Quantum Mechanics?

    Hello Homework Statement For a free particle moving in one dimension, divide the following set of operators into subsets of commuting operators: [P,x, H, p] Homework Equations The Attempt at a Solution I don't get the statement itself What does the set represents for the...
  23. F

    MHB Convergence of bounded linear operators

    Let (T_{n}) be a sequence in {B(l_2} given by T_{n}(x)=(2^{-1}x_{1},...,2^{-n}x_{n},0,0,...). Show that T_{n}->T given by T(x)==(2^{-1}x_{1},2^{-2}x_{2},0,0,...). I get a sequence of geometric series as my answer for the norm, but not sure whether that's correct.
  24. Doofy

    Quantum harmonic oscillator, creation & annihilation operators?

    For a set of energy eigenstates |n\rangle then we have the energy eigenvalue equation \hat{H}|n\rangle = E_{n}|n\rangle. We also have a commutator equation [\hat{H}, \hat{a^\dagger}] = \hbar\omega\hat{a}^{\dagger} From this we have \hat{a}^{\dagger}\hat{H}|n\rangle =...
  25. G

    Why do we conjugate operators in QFT?

    Why do we multiply some operator A both on the left and on the right with, say, A and A^(-1) in order to perform some kind of conjugation? If it helps, the example I'm thinking of is the relationship between Schrodinger and Heisenberg operators in QFT. Thanks.
  26. lonewolf219

    How to determine the product of two Hermitian operators is Hermitian

    Let's say we have operator X that is Hermitian and we have operator P that is Hermitian. Is the following true: [X,P]=ihbar This is the commutator of X and P. This particular result is known as the canonical commutation relation. Expanding: [X,P]=XP-PX=ihbar This result indicates that...
  27. R

    How Do You Find \left\langle\psi|a_1\right\rangle in Matrix Representation?

    Homework Statement This is quite a long problem, and I have most of it figured out, but I am getting stuck on the very last part of the problem. My problem is I do not understand how to find \left\langle\psi|a_1\right\rangle in the very last line. Is...
  28. snoopies622

    Finding the operators for time derivatives of observables

    Looking through this matrix approach to the quantum harmonic oscillator, http://blogs.physics.unsw.edu.au/jcb/wp-content/uploads/2011/08/Oscillator.pdf especially the equations m \hat{ \ddot { x } } = \hat { \dot {p} } = \frac {i}{\hbar} [ \hat {H} , \hat {p} ] I'm getting the impression...
  29. Q

    Expectation values with annihilation/creation operators

    Homework Statement Calculate <i(\hat{a} - \hat{a^{t}})> Homework Equations |\psi > = e^{-\alpha ^{2}/2} \sum \frac{(\alpha e^{i\phi })^n}{\sqrt{n!}} |n> \hat{a}|n> = \sqrt{n}|n-1> I derived: \hat{a}|\psi> = (\alpha e^{i\phi})^{-1}|\psi> The Attempt at a Solution...
  30. Shindo

    Use of differentiation operators?

    In Calculus, I am studying differentiation at the moment. The two equations is the basic Derivative function: (f(x+h)-f(x))/h and the alternative formula: (f(z)-f(x))/(z-x); and I can see how they both have their own purposes for finding the tangent line and such; but when will differentiation...
  31. H

    SHO ladder operators & some hamiltonian commutator relations

    Homework Statement For the SHO, find these commutators to their simplest form: [a_{-}, a_{-}a_{+}] [a_{+},a_{-}a_{+}] [x,H] [p,H] Homework Equations The Attempt at a Solution I though this would be an easy problem but I am stuck on the first two parts. Here's what I did at first...
  32. N

    Trying to interpret matrix representations of operators

    Say I have a 3x3 operator Q and I find its eigenvectors and eigenvalues. Now i know that those eigenvectors are the same as eigenfunctions so if i act on them with Q i will get the corresponding eigenvalue. What the question I am trying to solve asks is, Measure the quantity Q in state [b]...
  33. M

    Eigenfunction of all shift operators

    Prove that if a continuous function e\left( x \right) on \mathbb{R} is eigenfunction of all shift operators, i.e. e\left( x+t \right) = \lambda_t e\left( x \right) for all x and t and some constants \lambda_t , then it is an exponential function, i.e. e\left( x \right)= Ce^{ax} for some...
  34. B

    Can Hermitian Operators Commute if Their Commutator is Also Hermitian?

    Homework Statement [A,B] = C and operators A,B,C are all hermitian show that C=0 Homework Equations The Attempt at a Solution Since it is given that all operators are hermitian I know that A=A' B=B' and C=C' so i expanded it out to AB-BA=C A'B'-B'A'=C (BA)' - (AB)'=C...
  35. G

    Help on the expectation value of two added operators

    Hi everyone, I was just working on some problems regarding the mathematical formalism of QM, and while trying to finish a proof, I realized that I am not sure if the following fact is always true: Suppose that we have two linear operators A and B acting over some vector space. Consider a...
  36. snoopies622

    How to go from Heisenberg operators to Schrödinger operators

    It is obvious to me how \hat {x} = x; \hspace{5 mm} \hat {p}_x = -i \hbar \frac {\partial} {\partial x} implies [ \hat {x} , \hat {p}_x ] = i \hbar and I can accept that these two formulations are mathematically equivalent, but I do not know how in general (or even in this specific...
  37. T

    Matrix representations of angular momentum operators

    Homework Statement Write down the 3×3 matrices that represent the operators \hat{L}_x, \hat{L}_y, and \hat{L}_z of angular momentum for a value of \ell=1 in a basis which has \hat{L}_z diagonal. The Attempt at a Solution Okay, so my basis states \left\{\left|\ell,m\right\rangle\right\}...
  38. H

    Domain of Sturm-Liouville operators

    Hello, folks, A Sturm-Liouville operator is typically defined not on the whole space of C^2 functions, but rather on some subspace described by boundary conditions. My question is: are those subspaces closed (hence complete, hence Hilbert) in L^2? In case of an affirmative answer, how can...
  39. G

    Locally bounded linear differential operators

    The following is a problem statement. locally bounded (or locally (weakly) compact) differential operators of the Schwartz space of smooth functions on a sigma-compact manifold I realize this is very abstract. I expect the solution to be just as abstract. Thanks in advance.
  40. A

    Using operators and finding expectation value

    Homework Statement The expectation value of the time derivative of an arbitrary quantum operator \hat{O} is given by the expression: d\langle\hat{O}\rangle/dt\equiv\langled\hat{O}/dt\rangle=\langle∂\hat{O}/∂t\rangle+i/hbar\langle[\hat{H},\hat{O}]\rangle Obtain an expression for...
  41. G

    Commutation relation of the creation/annihilation operators in a field

    Hello, I'm having trouble calculating this commutator, at the moment I've got: \left[a_{p},a_{q}^{\dagger}\right]=\left[\frac{i}{\sqrt{2\omega_{p}}}\Pi(p)+\sqrt{\frac{w_p}{2}}\Phi(p),\frac{-i}{\sqrt{2\omega_{p}}}\Pi(p)+\sqrt{\frac{w_p}{2}}\Phi(p)\right]=i\left[\Pi(p),\Phi(q)\right]=i\int...
  42. C

    How to apply ladder operators?

    The total energy of a particle in a harmonic oscillator is found to be 5/2 ~!. To change the energy, if i applied the lowering operator 4 times and then the raising operator 1 times successively. What will be the new total energy? i want the calculation please
  43. A

    Differentiation with convolution operators

    Hello, I have really been banging my head the whole day and trying to figure this derivative out. I have a function of the following form: F = W * (I.J(t)) - (W * I).(W*J(t)) where I and J are two images. J depends on some transformation parameters t and W is a gaussian kernel with some fixed...
  44. L

    Do Tensor Product Properties Hold in Infinite Dimensional Hilbert Spaces?

    Is this correct in infinite dimensional Hilbert spaces? ## (\hat{A}_1 \otimes \hat{A}_2)^{-1}=\hat{A}^{-1}_1 \otimes \hat{A}^{-1}_2 ## ## (\hat{A}_1 \otimes \hat{A}_2)^{\dagger}=\hat{A}^{\dagger}_1 \otimes \hat{A}^{\dagger}_2 ## ## (\hat{A}_1 +\hat{A}_2) \otimes \hat{A}_3=(\hat{A}_1 \otimes...
  45. S

    What's the deal on infinitesimal operators?

    Is there a treatment of "infinitesimal operators" that is rigorous from the epsilon-delta point of view? In looking for material on the infinitesimal transformations of Lie groups, I find many things online about infinitesimal operators. Most seem to be by people who take the idea of...
  46. Physics Monkey

    How will things change after irrelevant operators are confirmed?

    I want to consider a thought experiment: Suppose, at some point in the near future, the effects of irrelevant operators in the standard model are firmly confirmed by experiment. In other words, we see some effect, perhaps the muon g-2, which simply cannot be accounted for without including...
  47. C

    Spherical tensor operators' commutation with lowering/raising operator

    I'm studying Shankar's book (2nd edition), and I came across his equation (15.3.11) about spherical tensor operators: [J_\pm, T_k^q]=\pm \hbar\sqrt{(k\mp q)(k\pm q+1)}T_k^{q\pm 1} I tried to derive this using his hint from Ex 15.3.2, but the result I got doesn't have the overall \pm sign on the...
  48. G

    Calculating Correlation of Composite Operators

    I have probably a silly question about correlation functions of composite operators. Why can't you just calculate a correlator with fields at different points x1, x2, x3, ... and then set a couple of the points equal at the end of the calculation to get the result? e.g., \langle 0...
  49. D

    Angular momentum operators on matrix form

    Homework Statement Hi. I'm given a 3-dimensional subspace H that is made up of the states |1,-1\rangle, |1,0\rangle and |1,1\rangle with the states defined as |l,m\rangle and l=1 as you can see. The usual operator relations for L_{z} and L^{2} applies, and also: L_{+} = L_{x}+iL_{y} L_{-} =...
  50. lonewolf219

    Creation Operators application

    Can creation operators be used to find a matrix representation in a larger dimension? Is that maybe how I could find the 3D representation for SU(2) ?
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