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. P

    Field Operators in Klein-Gordon theory

    Currently I am working through a script concerning QFT. To introduce the concept of canonical filed quantisation one starts with the (complex valued) Klein-Gordon field. I think the conept of quantising fields is clear to me but I am not sure if one can claim that the equations of motion for the...
  2. N

    Linear Algebra - Differentiation Operator on P_3

    Homework Statement I have a differentiation operator on P_3, and: S = {p \in P_3 | p(0) = 0}. I have to show that 1) D : P_3 -> P_2 is not one-to-one. 2) D: S -> P_3 is one-to-one. 3) D: S -> P_3 is not onto. The Attempt at a Solution For #1, I want to show that our...
  3. H

    MATLAB How to Handle Zero Values in MATLAB Arrays?

    I solved my last problem, however, I have another question with regards to logical operators in MATLAB. Suppose I have four column arrays "one," "two," "three," and "four." Each array contains 500 scalar values. How can I say: If anyone of these scalar values are equal to zero then...
  4. G

    Differentiation of an exponential with operators (Peskin p.84)

    Does anyone know how to differentiate an exponential, which has an operator in its power? I found it quite a trouble in Peskin's QFT (page 84, formulas (4.17), (4.18)). Here we have these two formulas of Peskin: U\left( t,t_{0}\right)=e^{iH_{0}\left( t-t_{0}\right) }e^{-iH\left(...
  5. maverick280857

    Commuting Operators in Sequential Stern Gerlach Experiment

    Hi everyone How do I show that the expression \sum_{b'}|\langle c'|b'\rangle|^{2}|\langle b'|a'\rangle|^{2} = \sum_{b'}\langle c'|b'\rangle\langle b'|a'\rangle \langle a'|b'\rangle \langle b'|c'\rangle equals the expression |\langle c'|a'\rangle|^{2} = |\sum_{b'}\langle c'|b'\rangle...
  6. E

    Field operators - how do they work?

    It seems to me that in the quantization of a classical field, one first takes the Fourier transform of the field to put it in frequency space: F \left(X, \omega \right) = \int f(X,t)e^\left(-i \omega t\right) then multiply by the annihilation and creation operators for a given wavelength: F...
  7. L

    Linear Algebra: Positive Operators

    Homework Statement Let A and B be nxn positive self-adjoint matrices such that for all x \in Cn, x*Ax = x*Bx. Prove that A = B. Equivalently, prove that if A, B are positive operators on H such that <Ax,x> = <Bx,x> \forall x \in H, then A = B. Hint: See Lemma 2.12. Homework Equations...
  8. F

    Bit shifting and bitwise operators

    Homework Statement folks, I have a small problem understanding a function as to what its doing: I have run this program in C++. I will comment the lines of code as per my understanding. Your insight would be useful unsigned int myfunc(unsigned int n) { // for n here I took 1200...
  9. M

    Strange definition of regularization of Operators

    surfing the web and arxiv i found the strange formula lnA= \frac{d^{n}}{ds^{n}} \frac{s^{n-1}}{n! A^{s}} my question is .. where does this formula come from ?? here 'n' is supposed to be a finite parameter we must define to avoid the divergences, is it valid for non-renormalizable or...
  10. A

    Anderson Hamiltonian (product of number operators) in 1st quantization?

    In the Anderson model, it cost an energy Un_{\Uparrow}n_{\Downarrow} for a quantum dot level to be occupied by two electrons. Here n_{\Uparrow} is the second quantized number operator, counting the number of particles with spin \Uparrow. I need the term Un_{\Uparrow}n_{\Downarrow} in first...
  11. M

    Linear algebra+ linear operators

    Homework Statement In R^{3} ||x||= a_{1}*|x_{1}|+ a_{2}*|x_{2}|+ a_{3}*|x_{3}|. where a_{i}>0 What is ||A||(indused norm = sup||Ax|| as ||x||=1). (Suppose we know the coeffisients of the matrix/operator A)?? Homework Equations The Attempt at a Solution
  12. H

    Operators, normalised eigenstates and the generalised uncertainty relation

    Homework Statement Hi guys! Many time reader, first time poster... I've struggled big time with the following. Any advice at all would be great. I'm so muddled, it's just not funny any more... (plus I'm not really familiar with who to write the mathematic script so please be patient) I...
  13. T

    Are My Raising and Lowering Operator Calculations Correct?

    [SOLVED] raising and lowering operators Homework Statement http://img125.imageshack.us/img125/2923/85098487ch9.jpg The Attempt at a Solution I expand a+ and a-, introduce the wavefunction and then substitute the values given at the very end to give...
  14. W

    Expectation values and operators.

    i'm just not sure on this little detail, and its keeping me from finishing this problem. take the arbitrary operator \tilde{p}^{n}\tilde{y}^{m} where p is the momentum operator , and x is the x position operator the expectation value is then <\tilde{p}^{n}\tilde{y}^{m} > is this the same...
  15. G

    Proving Compactness of Hilbert-Schmidt Operators in a Seperable Hilbert Space

    Hi there, Can anyone give me an hint/idea of how to prove Hilbert-Schmidt operators are compact? More specifically, if X is a seperable Hilbert space and T:X->X is a linear operator such that there exists an orthonormal basis (e_{n}) such that \sum_{n} ||T(e_{n})||^{2}<\infty then show that T...
  16. G

    Self-Adjoint Operators problem

    Homework Statement T a linear operator on inner product space V and W a T-invariant subspace of V. Then if T is self-adjoint then Tw is self-adjoint. Homework Equations Thm: T is self-adjoint iff \exists an orthonormal basis for V consisting of e-vectors of T. The Attempt at a...
  17. S

    Linear Algebra - Normal Operators

    Homework Statement Prove that if T in L(V) is normal, then Ker(Tk) = Ker(T) and Im(Tk) = Im(T) for every positive integer k. Homework Equations The Attempt at a Solution Since T is normal, I know that TT* = T*T, and also that ||Tv|| = ||T*v|| and <Tv, Tv> = <T*v, T*v>. Ker(T) is the...
  18. M

    Why Does the Hamiltonian Matrix Element <L|H|L> Equal E0?

    Homework Statement we shall describe a simple model for a linear molecule, say, CO2. the states |L>, |C>,|R> are the eigenstates of D operator (corresponds to dipole moment) D|L>=-d|L> , D|C>=0 , D|R>= +d|R>. When the electron is localized exactly on the carbon atom, its energy is E1...
  19. S

    Linear Algebra: Geometric Interpretation of Self-Adjoint Operators

    Homework Statement I'm not interested in the proof of this statement, just its geometric meaning (if it has one): Suppose T \in L(V) is self-adjoint, \lambda \in F, and \epsilon > 0. If there exists v \in V such that ||v|| = 1 and || Tv - \lambda v || < \epsilon, then T has an...
  20. C

    Proving that the Composition of Two Self-Adjoint Operators is Self-Adjoint

    Homework Statement Prove or give a counterexample: the product of any two self-adjoint operators on a finite-dimensional inner-product space is self-adjoint.Homework Equations The only two equations I've used so far are: \left\langle T v, w\right\rangle = \left\langle v, T^{*}w\right\rangle and...
  21. S

    Linear Algebra - Self-adjoint Operators

    Homework Statement Make P2(R) into an inner-product space by defining <p, q> = \int_0^1p(x)q(x)dx. Define T in L(P2(R)) by T(a_0 + a_1*x + a_2*x2) = a_1*x. (a) Show that T is not self-adjoint. (b) The matrix of T with respect to the basis (1, x, x2) is \left( \begin{array}{ccc} 0 & 0 & 0\\ 0...
  22. J

    Creation/annihilation operators

    For a system of N non-interacting bosons we start with the tensor product of single particle states \otimes_{n=1}^N | \alpha_i \rangle and then, due to the indistinguisability of the particles, symmetrize to obtain the occupation number state | n_1,n_2,\ldots,n_k\rangle = \frac{1}{\sqrt{N...
  23. J

    Operator Rotation: Expressing in New Reference Frame

    Suppose we know the matrix elements of an operator with respect a given cartesian reference frame L. If we know the sequence of rotations going from L to some other reference frame L', what is the expression for the operator in the new reference frame. Let R be the required rotation and...
  24. F

    Quantum Field Theory: Field Operators and Lorentz invariance

    [SOLVED] Quantum Field Theory: Field Operators and Lorentz invariance Hi there, I am currently working my way through a book an QFT (Aitchison/Hey) and am a bit stuck on an important step in the derivation of the Feynman Propagator. My problem is obviously that I am not a hard core expert...
  25. H

    Projection Operators on Vector Spaces: Clarifying Mistakes

    Supposing we have a vector space V and a subspace V_1\subset V. Suppose further that we have two different direct sum decompositions of the total space V=V_1\oplus V_2 and V_1\oplus V_2'. Given the linear projection operators P_1, P_2, P_1', P_2' onto these decompositions, we have that...
  26. J

    Infinite Well: Ladder Operators for Simplified Expression

    Is there a simple expression for the ladder operators, in terms of x and -i\hbar\partial_x, for the infinite potential well? After some attempts, I couldn't figure out any nice operators that would map functions like this \sin\frac{\pi n x}{L} \mapsto \sin\frac{\pi(n\pm 1)x}{L}.
  27. M

    Second Quantization and Field Operators

    When defining a field operator, textbooks usually say that one can define an operator which destroys (or creates) a particle at position r. What does this really mean? Are they actually referring to destroying (or creating) a state who has specific quantum numbers associated with the geometry...
  28. O

    Relation between a measurement and the operators

    Now, here is the problem. (Capital letters indicate operators, lower letters are states, * indicates Hermitian conjugate) Say we know that state | p > = cos(a) |0> + sin(a) |1> (0<a<PI, a is in R) Two operators : M1= |0><0| , M2=|1><1|, apperatantly they satisfy the...
  29. T

    Please help Give the following operators:

    Ive tried this quantum mechanic problem but I am not getting the right anwser: a-operator = [x-operator + i (complex #)] (p-operator) / (square root of 2) and a-operator ^ t = x-operator - i (p-operator) / square root of 2 where x operator is the position operator and p operator is...
  30. S

    Linear Operators: False for Non-Finite Dimensional Vector Spaces

    Let T be a linear operator on a finite dimensional vector space V, over the field F. Suppose TU = I, where U is another linear operator on V, and I is the Identity operator. It can ofcourse be shown that T is invertible and the invese of T is nothing but U itself. What I want to know is an...
  31. S

    Understanding Curl in 3D: Using Vector Operators & Components

    Can anyone explain to me how to expand this expression for curl which I find in the GR book I'm reading (by Hobson, Efstathiou and Lasenby, page 71)? In a section entitled Vector Operators in Component Form they state the curl as a "rank-2 antisymmetric tensor with components": (curl)ab =...
  32. Q

    Leibniz's Operators: True or False?

    I heard something about the well known Leibniz notation of calculus, and I thought that you guys would be able to tell me if it's a load of hogwash or not. The geist of it is this: \mathrm d and \int are actually operators, with \mathrm d being an operator that creates an infinitesimal from a...
  33. P

    Boolean operators in SQL - Correct Syntax?

    Hi all, Trying to write an SQL query for the Sloan Digital Sky Survey that uses the NOT operator, and failing miserably. Basically, I'm making photometric cuts in 4-d colour space, and I currently have a selection of inequalities that select enclosed regions of colour space. However, I...
  34. R

    Energy raising/lowering operators, algebra

    \hat{x} = \left(\frac{\hbar}{2wm}\right)^{1/2}(\hat{a} + \hat{a}^{+}) \hat{p} = -i\left(\frac{\hbar wm}{2}\right)^{1/2}(\hat{a} - \hat{a}^{+}) I'm trying to demonstrate that \hat{H} = (\hat{a}^{+}\hat{a} + \frac{1}{2})\hbar w where \hat{H} = \frac{1}{2m} \hat{p}^{2} +...
  35. B

    Solving a max() Function with Binary Operators

    Hey i was wondering if someone could help me express this using standard binary operators. f(x,y,z)=\frac{max(0, (x-y) )}{z} i.e. Eliminate the max() function and write it using proper math. EDIT: max(a,b) simply chooses the largest value of the two variables.
  36. Gib Z

    Differentiation operators similar to exponents?

    I was just messing around on another problem I was trying to solve for someone in the homework forums when I stumbled on this: If we denote the n-th derivative the same way we do for exponents, eg the second derivative of f will be denoted by f^2, and the original function as its zero-th...
  37. L

    Raising and lowering operators for spin

    When we set the raising and lowering operators for spin to be S_{\pm} = S_x \pm i S_y, what convention are we following (i.e. why is the first term taken to be S_x and the second taken to be S_y)?
  38. R

    Expectation Values of Spin Operators

    [SOLVED] Expectation Values of Spin Operators Homework Statement b) Find the expectation values of S_{x}, S_{y}, and S_{z} Homework Equations From part a) X = A \begin{pmatrix}3i \\ 4 \end{pmatrix} Which was found to be: A = \frac{1}{5} S_{x} = \begin{pmatrix}0 & 1 \\ 1 & 0...
  39. E

    Deciphering Confusing Differential Operator Problems

    I have two problems and I don't know what they want to tell. Please tell me what do you think 1. We define operator L[x]=a(t)\ddot{x}+b(t)\dot{x}+c(t)x in C^{2}(I) function space. Proof that \frac{\partial}{\partial\lambda}L[x]=L\left[\frac{\partial x}{\partial\lambda}\right]. ¿What do you...
  40. J

    Inner products, operators, equality

    Is it true, that if in Hilbert space, operators T and S satisfy (Tf|f)=(Sf|f) for all f in H, then T=S? I think it is clear, that if (Tf|g)=(Sf|g) is true for all f and g in H, then T=S, but I'm not sure if it is sufficient to only allow g=f.
  41. N

    Raising and lowering operators / spherical harmonics

    This isn't exactly a part of any problem, but a part of a generic principle. I don't understand the use of raising and lowering operators. L_{^+_-}=\hbar e^{^+_- i l \phi}({^+_-}\frac{\partial}{\partial \theta}+ i cot \theta \frac{\partial}{\partial \phi}) So how does one use L_{^+_-}Y_l^m...
  42. T

    Expectation value using ladder operators

    I wonder if someone could examine my argument for the following problem. Homework Statement Using the relation \widehat{x}^{2} = \frac{\hbar}{2m\omega}(\widehat{A}^{2} + (\widehat{A}^{+})^{2} + \widehat{A}^{+}\widehat{A} + \widehat{A}\widehat{A}^{+} ) and properties of the ladder operators...
  43. M

    In QM operators, why [YPz,YPx]=0, [ZPy,ZPy]=0 [X,Py]=0 [Y,Pz]=0, etc

    in the quantum mechanical operators : why : [YPz,YPx]=0 [ZPy,ZPy]=0 [X,Py]=0 [Y,Pz]=0 [Z,Py]=0
  44. J

    Help with differential operators

    Homework Statement This is a problem about differential operators, but I don't really get the notation used. I have L1 = (d/dx + 2) and L2 = (d/dx - 1) Find L1(xe^-2x) Show that L1L2 = L2L1 and find L1L2 in terms of d/dx, d2/dx2, etc. Homework Equations The Attempt at a...
  45. E

    What are the eigenvalues of L operators?

    Hi Homework Statement We're given the operators Lx, Ly and Lz in matrix form and asked to show that they have the correct eigenvalues for l=1. Obviously no problem determining the values and Lz comes out right, however we've never actually seen the e.v.s for Lx and Ly. Homework...
  46. S

    How can test functions help understand commutation relations?

    So I was reading from my quantum book (Gasiorowicz) and I ame across this sentence: [p^2, x] = p [p, x] + [p, x] p = \frac{2\hbar}{i} p I don't understand this. I know that p = -i \hbar \frac{\partial}{\partial x} , but I can't see how to get that expression...I just come up with...
  47. J

    Are These Mappings True Linear Operators?

    [SOLVED] Linear Operators Oops, nevermind I figured out my mistake. Homework Statement Determine which of the following mappings T: P1 -> p1 over R are linear operators. 1) T(a0 + a1x ) = a0*x 2) T(a0 + a1x ) = a1a0 + a0*x The Attempt at a Solution My book states that if U = V (vector...
  48. Q

    Operators fields and classical fields

    Whats the intuition behind the concept of current operator in QFT and PP. For example i know that the charge operaor which correspond to space integral of J-o when acted upon a fock space of the field of given type gives the total charge in the field but what about the remaining components...
  49. N

    Hermitian operators in spherical coordinates

    Hi, I have a general question. How do I show that an operator expressed in spherical coordinates is Hermitian? e.g. suppose i have the operator i \partial /\partial \phi. If the operator was a function of x I know exactly what to do, just check \int_\mathbb{R} \psi_l^\ast \hat{A} \psi_m dx =...
  50. S

    How Do You Calculate Lx and Ly Using Spherical Harmonics in Quantum Mechanics?

    Homework Statement Obtain the angular momentum operators L_{x} and L_{y} in the basis of functions Y^{\pm1}_{1}(\theta,phi} and Y^{0}_{1}(\theta,phi}[/itex] in Lz representation2. The attempt at a solution To calculate the matrices for the Lx and Ly operators, do i simply have to take the...
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