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.

View More On Wikipedia.org
Recent contents Top users
  1. R

    Eigen functions/values for many-body Hamiltonian with creation/annihilation operators

    Problem: ----------- I’m trying to understand how to generally find Eigen functions/values (either analytically or numerically) for Hamiltonian with creation/annihilation operators in many-body problems. Procedures: -------------- 1. I setup a simple case of finite-potential well...
  2. M

    What is the significance of the Casimir operators in QCD?

    Hi folks, I was wondering if the two Casimir operators of the SU(3) color gauge group were of any physical significance, or corresponded to any familiar physical properties. For example, I know that in the Poincare group the two Casimirs correspond to mass and spin: is there a similarly...
  3. M

    Isometric operators- spectrum preserving?

    Hi all, I'm working on Taylor's text on scattering (a reference from Peskin and Schroeder). They define the Moller operators \Omega which are isometric, satisfying \Omega^{\dagger}\Omega=1 This is not necessarily the same as unitary in an infinite dimensional space, the difference being...
  4. L

    Interpretiing the Dolbeault operators

    The differential of a function may me interpreted a the the dual of its gradient. What is the interpretation of the Dolbeault operators?
  5. M

    Definition of fermionic annihilation operators

    Hi, I'm revising for an exam and I came across a past paper that has a question on annihilation operators, It asks what happens when acting on a wavefunction with a group of different creation/annhilation operators (all identical fermions.. It's quite simple apart from the fact that it...
  6. K

    Hermitian Operators: Finding Psi(p) from Psi(x)

    I recently thought of this, please excuse me if it is way off the mark! If I act on a state with a hermitian operator, am I able to find the psi(p) (momentum), where I had psi(x) (position) before (and wise versa)? Or does the operator do what it appears to do, and that is find the derivative...
  7. S

    Solving Ladder Operator Problem w/ 4 Terms

    Homework Statement I have been given the following problem - the expectation value of px4 in the ground state of a harmonic oscillator can be expressed as <px4> = h4/4a4 {integral(-infin to +infin w0*(x) (AAA+A+ + AA+AA+ + A+AAA+) w0 dx} I think I know how to proceed on other...
  8. D

    Diagonalizing Linear Operators: Understanding the Differences

    Homework Statement Let V be a n-dimensional real vector space and L: V --> V be a linear operator. Then, A.) L can always be diagonalized B.) L can be diagonalized only if L has n distinct eigenvalues C.) L can be diagonalized if all the n eigenvalues of L are real D.) Knowing the...
  9. M

    Hermitian operators without considering them as Matrices

    A Hermitian matrix is a square matrix that is equal to it's conjugate transpose. Now let's say I have a Hermitian operator and a function f: [ H.f ] The stuff in the square is the complex conjugate as the functions are in general complex. If I do not consider the matrix representation of...
  10. B

    Need a lot of help with vector fields/vector operators

    Homework Statement http://img818.imageshack.us/f/screenshot20110423at733.png/ http://img856.imageshack.us/f/screenshot20110423at733.png/ If it'll help you guys help me understand this, here are the solutions: http://img828.imageshack.us/f/screenshot20110423at752.png/ Homework Equations...
  11. C

    How Do Raising Operators Work in Quantum Mechanics?

    I don't understand the following step: using \hat{}a*\hat{}a = (\hat{}H/\hbarw ) -1/2 <n|\hat{}a*\hat{}a|n> = n<n|n>. my first thoughts were to use a|n> = sqrt n | n-1> but I don't think that's relevant if you sub in a*a and separate it into two expressions I don't see what good that would do
  12. C

    Homework SolutionQuantum Operators: Pr Y & Pr^2 Y

    Homework Statement I'm given the expression for the operator Pr Y Pr Y= -ih(bar) (1/r) d/dr (r Y) I want to find Pr^2 Y so I have dotted Pr with Pr I expect to get: -h(bar)^2 (1/r) d/dr [ Y(Y + r dY/dr)] but my notes have omitted the first Y in the above bracket and I...
  13. I

    Expectation values of spin operators

    Hi, I've found the expectation value of Sz, which is hbar/2 (|\psiup|2 - |\psidown|2) by using the formula: <Si> = <\psi|Si\psi> where i can bex, y or z and \psi is the 'spinor' vector. I tried to find Sx using the same formula, however, I could only get as far as: hbar/2 ((\psiup)*\psidown...
  14. M

    Bounded Operators: Linearity & Inequality

    a linear operator T: X -> Y is bounded if there exists M>0 such that: ll Tv llY \leq M*ll v llX for all v in X conversely, if i know this inequality is true, is it always true that T: X ->Y and is linear?
  15. S

    Proving Non-Linearity of y2: Linear Operators Homework

    Homework Statement Show that y2 is non-linear. Homework Equations ^O (ay1 +by2) = a ^O(y1) + b ^O(y2). The Attempt at a Solution No idea!
  16. Q

    Non-linear Operators: Physical Reasons Explained

    Hi, I was wondering: What is the physical reason for only choosing linear operators to represent observables?
  17. D

    Manipulating Equations with Del Operators

    I'm trying to understand how to manipulate equations with del operators. If I have a equation like : div( A + B ) = div(E) and assume A,B,E are twice differential vectors do div cancel? can I say E = A + B? If I write is like this div( A + B - E ) = 0 div( A + B - (A + B)) = 0...
  18. M

    Complex Conjugate applied to operators?

    I have a rather fundamental question which I guess I've never noticed before: Firstly, in QM, why do we define the expectation values of operators as integral of that operator sandwiched between the complex conjugate and normal wavefunction. Why must it be "sandwiched" like this? From...
  19. T

    QM - Deriving the Ladder Operators' Eigenbasis

    I'm am trying to derive the relations: a|n\rangle=\sqrt{n}|n-1\rangle a^{\dagger}|n\rangle=\sqrt{n+1}|n+1\rangle using just the facts that [a,a+]=1 and N|n>=|n> where N=a^{\dagger}a (which implies \langle n|N|n\rangle=n\geq 0). This is what I've done so far: [a,a^{\dagger}]=1 \Rightarrow...
  20. S

    In the reality how I perform the many kind of measurements, like operators p,q,E

    in the experimental side of QM, I know i can use a slit to measure the q. but what about p or E? and how to conciliate the measure with the theory?: after the measurement of a slit i'll measure q and the system will collapse in a autovector of q, like |q> but it will evolve like a...
  21. G

    Linear Algebra - Characteristic Polynomials and Nilpotent Operators

    Homework Statement If the characteristic polynomial of an operator T is (-1)^n*t^n, is T nilpotent? Homework Equations The Attempt at a Solution My first instinct for this question is that the answer is yes, because the matrix form of T must have 0's on the diagonal and must...
  22. G

    Characteristic Polynomials and Nilpotent Operators

    If the characteristic polynomial of an operator T is (-1)^n*t^n, is T nilpotent? My first instinct for this question is that the answer is yes, because the matrix form of T must have 0's on the diagonal and must be either upper triangular or lower triangular. This is what I found when I tried...
  23. A

    Quantum mechanics - creation and annihilation operators

    Homework Statement Evaluate <n|p^2|n> where p is the momentum operator for the quantised harmonic oscillator. Homework Equations creation operator: a+|n>=sqrt(n+1)|n+1> annihilation operator: a|n>=sqrt(n)|n-1> The Attempt at a Solution the operator p can be defined in terms of...
  24. I

    How Do You Determine Linear Transformations in R^2?

    Homework Statement If L((1,2)^T) = (-2,3)^T and L((1, -1)T) = (5,2)T determine L((7,5)T) Homework Equations If L is a linear transformation mapping a vector V into W, it follows: L(v1 + v2) = L(v1) +L(v2) (alpha = beta = 1) and L (alpha v) = alpha L(v) (v = v1, Beta = 0)...
  25. K

    Where can I learn how to manipulate operators?

    Nice to be back here at PF and to physics after a year off in the software industry. Now it's time to catch up again :) I feel like I never really get the grasp of manipulating operators. In QM there's a lot of trixing and mixing going on, and I really would like to learn to do the magic...
  26. P

    Operator-Valued Functions in Quantum Field Theory: Degrees of Freedom?

    Is it correct to express quantum field theory as "operator valued function" or "operator function" to spacetimepoints. Also, how value of field at each point act as a separate degrees of freedom.
  27. ShayanJ

    Can an operator change a wave equation without changing the system?

    I read somewhere that the meaning of applying an operator to a wave equation is measuring the quantity associated with that operator.And because the result is a function different than the wave function,the system is changed because of the measurment. But there is a problem here.If the above...
  28. N

    Hermitian operators and cummutators problem

    A,B and C are three hermitian operators such that [A,B]=0, [B,C]=0. Does A necessarily commutes with C?
  29. Fredrik

    Functional analysis, projection operators

    Homework Statement I want to understand the proof of proposition 7.1 in Conway. The theorem says that if \{P_i|i\in I\} is a family of projection operators, and P_i is orthogonal to P_j when i\neq j, then for any x in a Hilbert space H, \sum_{i\in I}P_ix=Px where P is the projection...
  30. U

    Quantum Mechanics, commutators and Hermitian Operators

    Homework Statement Suppose that the commutator between two Hermitian operators â and \hat{}b is [â,\hat{}b]=λ, where λ is a complex number. Show that the real part of λ must vanish. Homework Equations Let A=â B=\hat{}b The Attempt at a Solution AΨ=aΨ BΨ=bΨ...
  31. A

    Matrix Elements of Operators & Orthonormal Basis Sets

    So, the rule for finding the matrix elements of an operator is: \langle b_i|O|b_j\rangle Where the "b's" are vector of the basis set. Does this rule work if the basis is not orthonormal? Because I was checking this with regular linear algebra (in R3) (finding matrix elements of linear...
  32. T

    Quantum Mechanics - Ladder Operators

    I'm trying to show that \sum_{m=0}^\infty \frac{1}{m!} (-1)^m {a^{\dagger}}^m a^m =|0 \rangle\left\langle 0| Where a and {a^{\dagger}} denote the usual annihilation and creation operators. The questions suggests acting both sides with |n> but even if I did that and showed LHS=...=RHS then that...
  33. T

    Quantum Mechanics - Ladder Operators

    I'm trying to show that N=a^\dagger a and K_r=\frac{a^\dagger^r a^r}{r!} commute. So basically I need to show [a^\dagger^r a^r,a^\dagger a]=0. I'm not quite sure what to do, I've tried using [a,a^\dagger] in a few places but so far haven't had much success.
  34. Fredrik

    Finite Rank Operators: Prove T* Has Finite Rank

    This is probably easy. It's really annoying that I don't see how to do this... A finite rank operator (on a Hilbert space) is a bounded (linear) operator such that its range is a finite-dimensional subspace. I want to show that if T has finite rank, than so does T*. I'm thinking that the...
  35. G

    Is B(X,Y) a Vector Space of Bounded Linear Operators over the Same Scalar Field?

    Homework Statement Show L(X,Y) is a vector space. Then if X,Y are n.l.s. over the same scalar field define B(X,Y) = set of all bounded linear operators for X and Y Show B(X,Y) is a vector space(actually a subspace of L(X,Y) Homework Equations The Attempt at a Solution im not sure if i have...
  36. D

    Transformation of electron spin vectors and operators - a problem

    Homework Statement I am struggling to understand spin transformations and have used Sakurai's method of |new basis> = U |old basis> to change basis vectors and hence should have Sz' = Udagger Sz U to transform the operator. I thought this should give Sz' = Sy in the workings (see...
  37. T

    Quantum Mechanics - Unitary Operators and Spin 1/2

    Hi, I'm doing question 2/II/32D at the top of page 68 here (http://www.maths.cam.ac.uk/undergrad/pastpapers/2005/Part_2/list_II.pdf ). I have done everything except for the last sentence of the question. This is what I have attempted so far: |\chi\rangle=|\uparrow\rangle=\left(...
  38. T

    Step operators for harmonic oscillator

    Hi! Info: This is a rather elementary question about the creation a(+) and annihilation (a-) operators for the 1D H.O. The problem is to calculate the energy shift for a given state if the weak perturbation is proportional to x⁴. Using first order perturbation theory for the...
  39. B

    Bosonic operators and fourier transformation.

    If a_m = \frac{1}{\sqrt{N}} \sum_k e^{-ikm}a_k where a_k is a bosonic operator fulfilling [a_k, a_{k'}^{\dagger}] = \delta_{kk'} then is the product a_m a_{m+1} = \frac{1}{N} \sum_k e^{-ikm}e^{-ik(m+1)}a_k a_{k+1} ? Because that's what I'm doing but it doesn't lead me anywhere near to...
  40. Y

    The Klein-Gordon field as harmonic operators

    I am reading through 'An Introduction to QFT' by Peskin & Schroeder and I am struggling to follow one of the computations. I follow writing the field \phi in Fourier space ϕ(x,t)=∫(d^3 p)/(2π)^3 e^(ip∙x)ϕ(p,t) And the writing the operators \phi(x) and pi(x) as ϕ(x)=∫(d^3 p)/(2π)^3...
  41. A

    Linear Operators: Relationship Between Action on Kets & Bras

    This is basically more of a math question than a physics-question, but I'm sure you can answer it. My question is about linear operators. If I write an operator H as (<al and lb> being vectors): <alHlb> What is then the relationship between H action the ket and H action on the bra. Is this for...
  42. A

    What is a Hermitian Operator? Explained & Proven

    Hi, this is actually more a math-problem than a physics-problem, but I thought I'd post my question here and see if anyone can help me. So I'm writing an assignment in which I have to define, what is understood by a hermitian operator. My teacher has told me to definere it as: <ϕm|A|ϕn> =...
  43. Y

    Solution to Operators Problem Using the Operator Expansion Theorem

    Homework Statement Use the operator expansion theorem to show that Exp(A+B) = Exp(A)\astExp(B)\astExp(-1/2[A,B]) (1) when [A,B] = \lambda and \lambda is complex. Relationship (1) is a special case of the Baker-Hausdorff theorem. Homework Equations Operator expansion theorem...
  44. T

    Ladder operators for angular momentum

    This might be a basic question, but I'm having some difficulty understanding expectation values and ladder operators for angular momentum. <L+> = ? I know that L+ = Lx+iLy, but I don't know what the expectation value would be? Someone told me something that looked like this...
  45. Y

    Simultaneous diagonalization of two hermitian operators

    I decided to go over the mathematical introductions of QM again.The text I use is Shankar quantum, and I came across this theorem: "If \Omega and \Lambda are two commuting hermitain operators, there exists (at least) a basis of common eigenvectors that diagonalizes them both." in the proof...
  46. pellman

    Time independent operators and Heisenberg eq - paradox?

    Suppose we have time-dependent operator a(t) with the equal-time commutator [a(t),a^{\dag}(t)]=1 and in particular [a(0),a^{\dag}(0)]=1 with Hamiltonian H=\hbar \omega(a^\dag a+1/2) The Heisenberg equation of motion \frac{da}{dt}=\frac{i}{\hbar}[H,a]=-i\omega a implies...
  47. F

    Prove: Hermitian Operators (QR)*=R*Q*

    Homework Statement Prove: (QR)*=R*Q*, where Q and R are operators. (Bij * I mean the hermitian conjugate! I didn't know how to produce that weird hermitian cross) The Attempt at a Solution I have to prove this for a quantum physics course, so I use Dirac's notation with two random functions f...
  48. E

    Resolvents operators and integral equations

    Homework Statement I'm not clear exactly on how one computes the resolvent operator, given an integral operator. I was trying to practice by looking at some book examples and problems, and this one has me stuck. Consider u(x) = 1 + \int_0^x (y-x) u(y) dy = 1 + \int_0^x y u(y) dy -...
  49. M

    Commutative linear operators and their properties

    Can someone help me with this? When two linear operators commute, I know how to show that they must have at least one common eigenvector. Beyond this fact, what else can be said about commutative operators and their eigenvectors? Further, can they be diagonalized simultaneously (or actually, can...
  50. M

    What happens if two operators commute?

    I am trying to understand the idea of measurements on a system. Forgive me if any of my interpretations are incorrect...I'm hoping things can be cleared up. A measurement is taken on a system, represented by an operator, and this measurement changes the state of the system into a state...
Back
Top