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. M

    Stationary States in Griffiths Intro to QM

    I am referring to the section The Harmonic Oscillator in Griffiths's introductino to quantum mechanics (the older edition with the black cover). I understand how it all works, however there is a part that I am not sure about. How do we know when we apply a- or a+ (the ladder operators) to a...
  2. kini.Amith

    Commutator of function of operators

    According to my teacher, for any two operators A and B, the commutators [f(A),B]=[A,B]df(A)/dA and [A,f(B)]=[A,B]df(B)/dB He did not give any proof. I can easily prove this for the particular cases [f(x),p]=[x,p]df(x)/dx and [x,pn]=[x,p]npn-1 But I don't see how the general formula is true. I...
  3. M

    Understanding Adjoint Operators: A Helpful Explanation and Example

    hey pf! can you help me understand what an adjoint operator is? I've read lots of threads and other sites, but am having trouble. maybe you could give me an example? for example, does the operator d/dx have an adjoint? is asking this question completely stupid of me? thanks!
  4. M

    SU(2) operators to SU(N) generators for Heisenberg XXX

    A paper I'm reading says "Our starting point is the SU(N) generalization of the quantum Heisenberg model: H=-J\sum_{\langle i,j \rangle}H_{ij}=\frac{J}{N}\sum_{\langle i,j \rangle}\sum_{\alpha , \beta =1}^N J_{\beta}^{\alpha}(i)J_{\alpha}^{\beta}(j) The J_{\beta}^{\alpha} are the generators of...
  5. D

    Do AB and BA always exist in matrix multiplication?

    When performing matrix multiplication with 2 matrices A and B ;AB might exist but BA might not even exist. Hermitian operators can be thought of as matrices but in everything I have seen so far AB and BA always exist even though they can be different depending on the value of the commutator. Do...
  6. ShayanJ

    Total angular momentum operators

    Sometimes the concept of angular momentum is presented using the idea of total angular momentum J. In those cases, its always said that we have \vec{J}=\vec L + \vec S . But I can't understand how that's possible. Because orbital angular momentum operators are differential operators and so are...
  7. K

    Ladder operators and the momentum and position commutator

    When using Fourier's trick for determining the allowable energies for stationary states, Griffiths introduces the a+- operators. When factoring the Hamiltonian, the imaginary part is assigned to the momentum operator versus the position operator. Is there a reason for this? If : a-+ = k(ip +...
  8. carllacan

    Why don't creation and destruction operators conmute?

    Hi. I was wondering why creation and destruction operators a+ and a- do not conmute. Of course, I can show that they don't conmute by computing the conmutator [a+, a-] = -1. But I want to know the "physical" meaning of this. Isn't destruction/creation a symmetric transformation? We "go up...
  9. B

    Finding A Solution Using the Ladder Operators

    Hello, I am reading Griffiths Quantum Mechanics textbook, and am having some difficulty with a derivation on page 56. To me, there seems to be something logically wrong with his arguments, but I can not pin-point precisely what it is. To provide you with a little background, Griffiths is...
  10. gfd43tg

    Solving Conditional Operators Homework with Switch-Case

    Homework Statement Using the switch-case construction, write code that take a variable named Shape containing a string and assigns to the variable numSides the number of sides of the shape named in the variable Shape. Your code should be able to return the number of sides for a triangle...
  11. gfd43tg

    Test Score relational operators MATLAB

    Homework Statement Hello, I am working on problems 6-14 on the attached PDF. Don't be scared off, they are just one line of code each. I got number 6 correct, and I got partial credit on 7 and 8, but I am trying to figure out why it is not right. Homework Equations The Attempt at a...
  12. S

    Vector field (rotors and nabla operators)

    Homework Statement Find ##\alpha ## and ##p## so that ##\nabla \times \vec{A}=0## and ##\nabla \cdot \vec{A}=0##, where in ##\vec{A}=r^{-p}[\vec{n}(\vec{n}\vec{r})-\alpha n^2\vec{r}]## vector ##\vec{n}## is constant. Homework Equations The Attempt at a Solution ##\nabla \times...
  13. kq6up

    Understanding Hermitian Operators for QM Beginners

    I am a QM beginner so go easy on me. I have just noticed something. Let $$\hat{O}$$ be an hermitian operator. Then $$\left( \hat { O } \right) ^{ \dagger }\neq \hat { O } $$ when it is by itself. For example $$\left( \hat { p } \right) ^{ \dagger }=i\hbar \frac { \partial }{ \partial x...
  14. R

    Density Operators: What's the Copies of the Same System?

    Hi, there. I am a little confused about the following statement in Wikipedia. and it's about the density operators. "...As mentioned above, a state of a quantum system is given by a unit vector in a Hilbert space. More generally, if one has a large number of copies of the same system, then...
  15. carllacan

    Position operators and wavefunctions

    Homework Statement Find the eigenfunctions and the eigenvalues of the following Hamiltonian \hat{H} = \frac{1}{2m} \left ( \frac{ \hbar}{i} \vec{\nabla}-\frac{q}{c}(0, B_z x,0) \right ) ^2 = \frac{1}{2m} \left ( - \hbar^2 \vec{\nabla}^2-\frac{\hbar q}{ic}(\vec{\nabla}·(0, B_z\hat{x},0) +...
  16. L

    Function of operators. Series, matrices.

    Is it possible to write series ##\ln x=\sum_na_nx^n##. I am asking you this because this is Taylor series around zero and ##\ln 0## is not defined. And if ##A## is matrix is it possible to write ##\ln A=\sum_na_nA^n##. Thanks for the answer!
  17. R

    The dot or cross product of two operators acting on a state

    If a system is made up by two subsystems, for example, the atom and the photon. and let's assume the state of the atoms is described by |\phi\rangle, while the state of the photons can be described by |n\rangle, The Kronecker product of the |\phi\rangle and |n\rangle can be used to describe the...
  18. J

    CP Operators and Mesons: Investigating Boundaries

    Hi, I am currently going over this and got me thinking about a scanario where you have A -> BC Where A is S = 0, L=0, B is S = 1 L=0, C is S=1 L =0 (I'll use S = intrinsic spin, L = angular momentum, J = Total Angular momentum, |L-S|=< J =< L+S) Maybe such a decay doesn't exist, but I'm just...
  19. C

    Understanding tensor operators

    The definition of tensor operator that I have is the following: 'A tensor operator is an operator that transforms under an irreducible representation of a group ##G##. Let ##\rho(g)## be a representation on the vector space under consideration then ##T_{m_c}^{c}## is a tensor operator in the...
  20. C

    Raising and lowering operators of the Hamiltonian

    Homework Statement a) The operators ##a## and ##a^{\dagger}## satisfy the commutation relation ##[a,a^{\dagger}] = 1##. Find the normalization of the state ##|\psi \rangle = C (a^{\dagger} )^2 |0\rangle##, where the vacuum state ##|0\rangle## is such that ##a|0\rangle = 0## b)A one...
  21. M

    How do ladder operators generate energy values in a SHO?

    Hello, I am currently studying ladder operator for a simple harmonic operator as a method for generating the energy values. This seem like a simple algebra question I am asking so I do apologize but I just can't figure it out. Here are my operator definitions...
  22. I

    Help with Operators written as components.

    I would appreciate if someone could set me straight here. I understand if I have an arbitrary operator, I can express it in matrix component notation as follows: Oi,j = <vi|O|vj> Is it possible to get a representation of the operator O back from this component form. I'm more interested...
  23. maverick280857

    Sakurai Degenerate Perturbation Theory: projection operators

    Hi, So, I am working through section 5.2 of Sakurai's book which is "Time Independent Perturbation Theory: The Degenerate Case", and I see a few equations I'm having some trouble reconciling with probably because of notation. These are equations 5.2.3, 5.2.4, 5.2.5 and 5.2.7. First, we...
  24. M

    Angular momentum operators and eigenfunctions

    Homework Statement Homework Equations The Attempt at a Solution I have tried inserting the first wavefunction into Lz which gets me 0 for the eigenvalue for the first wavefunction. Is this correct? For the second wavefunction, I inserted it into Lz and this gets me -i*hbar*xAe^-r/a which...
  25. C

    Understanding Coupled Spin Operators

    Trying to get my head around this one. Given that you can have a proton and an electron in a hydrogen atom for example, and they can create a singlet or triplet configuration, with spin 1 and spin 0 respectively. The total spin operator can be derived as: S^2 = (Se + Sp)^2 = Se^2 + Sp^2 +...
  26. C

    Angular momentum Operators and Commutation

    So I understand the commutation laws etc, but one thing I can't get my head around is the fact that L^2 commutes with Lx,y,z but L does not. I mean if you found L^2 couldn't you just take the square root of it and hence know the total angular momentum. It seems completely ridiculous that you...
  27. C

    Multiplying out differential operators

    In this video at around 9:00 , Carl Bender demonstrates a method of solving y''+a(x)y'+b(x)y=0. He first rewrites it in terms of differential operators D2+a(x)D+b(x))y(x)=0, then factors it (D+A(x))(D+B(x))y=0 then multiplies it out to determine B(x). I thought we would get...
  28. J

    Differential forms and differential operators

    After read this stretch https://en.wikipedia.org/wiki/Closed_and_exact_forms#Vector_field_analogies, my doubts increased exponentially... 1. A scalar field correspond always to a 0-form? 1.1. The laplacian of 0-form is a 2-form? 1.2. But the laplacian of sclar field is another scalar field...
  29. Matterwave

    What is the disparity in the dimensionality of angular momenta?

    Hi guys, This is a problem which is bothering me right now. The angular momentum operators (Lx, Ly, Lz), when expressed in spatial rotations consists of derivatives in \theta and \phi. This would suggest that there are, at any point in space, only two linearly independent operators (since there...
  30. J

    Diferentiation and differential operators

    If the gradient of f is equal to differential of f wrt s: \vec{\nabla}f=\frac{df}{d\vec{s}} so, what is the curl of f and the gradient of f in terms of fractional differentiation?
  31. N

    How Does the Quantum Operator \(\hat{p}^2\) Derive from \(\hat{p}\)?

    Homework Statement Given that \hat{p} = -i\hbar (\frac{\partial}{\partial r} + \frac{1}{r}) , show that \hat{p}^2 = -\frac{\hbar^2}{r^2} \frac{\partial}{\partial r}(r^2 \frac{\partial}{\partial r}) Homework Equations Above The Attempt at a Solution I tried \hat{p}\hat{p} =...
  32. H

    Unitary Operator Inverse Transformation: Solving for a_m

    Hi everyone, I was hoping that someone might be able to tell me if what I'm doing is legit. Firstly, I start by saying that a unitary transform can be made between two sets of operators (this is defined in this specific way); b_{n} = \Sigma_{m} U_{mn}a_{m} (1) Now this is the bit I'm...
  33. F

    MHB Spectral decomposition of compact operators

    Let T be a compact operator on an infinite dimensional hilbert space H. I am proving the theorem which says that $Tx=\sum_{n=1}^{\infty}{\lambda}_{n}\langle x,x_{n}\rangle y_{n}$ where ($x_{n}$) is an orthonormal sequence consisting of the eigenvectors of $|T|=(T^*T)^{0.5}$, (${\lambda}_{n}$)...
  34. marcus

    Length and curvature operators in Loop gravity

    Most of us are familiar with the fact that in Loop gravity the area and volume observables have discrete spectrum. The discrete spectrum of the area operator, leading to a smallest positive measurable area, has lots of mathematical consequences that have been derived in the theory. It helps...
  35. C

    Simultaneous measuring of two operators

    Hello everybody. I am new here, and also new to quantum mechanics. This is the question to which I can't answer neither in mathematical nor physical way. a,b → observables (like position and momentum) A,B → corresponding operators. "It is possible for particles to be in a state of...
  36. Einj

    How Does the Second Quantized Field Operator Act on a Two-Fermion Wave Function?

    I have a doubt on the second quantization formalism. Suppose that we have two spin-1/2 fermions which can have just two possible quantum number, 1 and 2. Consider the wave function: $$ \psi(r_1,r_2)=\frac{1}{\sqrt{2}}\left(\psi_1(r_1)\psi_2(r_2)-\psi_1(r_2)\psi_2(r_1)\right). $$ The second...
  37. H

    Are coordinate operators Hermitian?

    I can't figure this one out given that the coordinate operator is continuous, it's hard to imagine "matrix elements". But presumably since the coordinates of the system (1d free particle) are always real valued, would this make the coordinate operator Hermitian?
  38. K

    Simultaneously diagonalize two operators

    Most part of the fundamental quantum mechanics rely upon finding some operators \hat{X} that commutes with hamiltonian and is able to simultaneously diagonalize \hat{X} and hamiltonian. Actually what do you mean by diagonalize simultaneously?? Is there any relation with diagonalize the...
  39. B

    MHB Invariant subspace for normal operators

    I have proved the spectral theorem for a normal operator T on an infinite dimensional hilbert space, and am now trying to deduce that T has non-trivial invariant susbspaces. Case 1: If the spectrum of T consists of a single point: My book says that if this is the case then the set of continuous...
  40. Q

    Transforming Operators with Matrix P

    I have two possible bases (a,b) and (a',b'). If I also have the transformation matrix P, such that P(a,b)=(a',b'), am I correct in assuming that I can change an operator A, from the (a,b) basis to the (a',b') basis by applying A' = P_transposed * A * P ?
  41. P

    How Do You Solve Quantum Operator Commutators?

    Homework Statement Hi,guys. I have a hard time understanding algebra and tricks of operators. So i have few examples: 1)[\hat{p}2x,xn] 2)[\hat{l}z,x],where \hat{l}z=x\hat{p}y-y\hat{p}x Homework Equations The Attempt at a Solution 1)[\hat{p}2x,xn]= [\hat{p}x \hat{p}x,xn]=...
  42. R

    Raising and Lowering Operators in the Lipkin Model

    Homework Statement I am trying to calculate the expectation value of an operator in the Lipkin model of nuclear physics. The background isn't important because my problem in really just a math problem. Homework Equations The anticommutation relation \begin{align*} a_{p\sigma}...
  43. P

    What does the operator A'A represent in image processing?

    Hello all, I hope this is the write sub-forum for this question. I have been looking at the Laplacian of a 2-D vector field. It is explained nicely by this Wikipedia article here. My question is more regarding how these operators work together. So, in the case of the Laplacian, it tells me...
  44. A

    Is the product rule on operators different from traditional calculus?

    Hey Guys, I regard two operators \Psi , \Phi , that don't commute. Does the product-rule, looks like that? $$\nabla (\Phi \Psi) = \Psi (\nabla \Phi) +\Phi (\nabla \Psi) $$ THX
  45. N

    Exploring Hermitean Operators and Their Role in Quantum Mechanics

    OK I'm not sure if this should go in the math or quantum forum, but as I'm learning these in introductory QM I post the questions here. Please move the thread if the section is inappropriate. Anyway, some questions: * What is an inner product space? * What is a hilbert space? * What are...
  46. N

    Why the generator operators of a compact Lie algebra are Hermitian?

    Why generator matrices of a compact Lie algebra are Hermitian?I know that generators of adjoint representation are Hermitian,but how about the general representaion of Lie groups?
  47. pellman

    Commutator for fermion operators?

    If we have two fermion operators with a known anti-commutator AB+BA, what do we do if we find ourselves with AB-BA in an equation? Does this automatically vanish for fermions? if not, is there anything we can say about in general?
  48. K

    Regarding the creation and annhilation operators in QFT

    Hello! I'm trying to understand QFT for the moment and have a question regarding the basic. So we have a vectorspace (Hilbertspace) of our states. The operator \phi(x) measures the amplitude at point x, whereas the operator \pi(x) measures the momentum density.. The ladder operator...
  49. A

    Norms of compositions of bounded operators between different spaces

    Suppose I have B: X\to Y and A: Y\to Z, where X,Y,Z are Banach spaces and B\in \mathcal L(X,Y) and A\in \mathcal L(Y,Z); that is, both of these operators are bounded. Does it follow that AB \in \mathcal L(X,Z) and \| AB \|_{\mathcal L(X,Z)} \leq \|A\|_{\mathcal L(Y,Z)} \|B\|_{\mathcal L(X,Y)}...
  50. N

    Dirac Notation and Hermitian operators

    Homework Statement Using Dirac Notation prove for the Hermitian operator B acting on a state vector |ψ>, which represents a bound particle in a 1-d potential well - that the expectation value is <C^2> = <Cψ|Cψ>. Include each step in your reasoning. Finally use the result to show the...
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