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. S

    How Does Angular Momentum Operate in Exponential Form?

    Hey! How does the operator of angular momentum operates in exponential form? $$ e^{-i\theta J}\vert l, m \rangle = ?? $$ where $$J\vert \Psi \rangle = J\vert l, m \rangle$$ and $$J^2\vert \Psi\rangle = \hbar^2 l(l+1)\vert \Psi\rangle $$ Also, how do you operate $$J_-$$ and $$J_+$$...
  2. M

    Operators in quantum mechanics

    Hi, We know the convergence of a series but what does it mean to say that "an operator converges or diverges"?
  3. Coffee_

    Fourier series, Hermitian operators

    (First of all I never saw Hilbert spaces in a mathematical class, only used it in intro QM so far, so please don't assume I know that much when answering.) Let's consider the Hilbert space on the interval [a,b] and the operator ##\textbf{L} = \frac{d^{2}}{dx^{2}} ##. Then ##\textbf{L}## is...
  4. gfd43tg

    Ladder operators to find Hamiltonian of harmonic oscillator

    Hello, I was just watching a youtube video deriving the equation for the Hamiltonian for the harmonic oscillator, and I am also following Griffiths explanation. I just got stuck at a part here, and was wondering if I could get some help understanding the next step (both the video and book...
  5. R

    Quantum Mechanics: Angular Momentum Operators

    Homework Statement Use the spin##-1## states ##|1,1\rangle, \ |1,0\rangle, \ |1, -1\rangle## as a basis to form the matrix representations of the angular momentum operators. Homework Equations ##\mathbb{\hat{S}}_+|s,m\rangle = \sqrt{s(s+1)-m(m+1)}\hbar|s,m+1\rangle##...
  6. amjad-sh

    Property related to Hermitian operators.

    Hello; I'm reading "principles of quantum mechanics" by R.Shankar. I reached a theorem talking about Hermitian operators. The theorem says: " To every Hermetian operator Ω,there exist( at least) a basis consisting of its orthonormal eigenvectors.Its diagonal in this eigenbasis and has its...
  7. D

    Harmonic oscillator in 2D - applying operators

    Hello, I juste don't know how this was done it is on the solutionnary of a very long exercise and i am not getting this calculation 1. Homework Statement <1,0| ax+ay++ax+ay+axay++axay|0,1> = <1,0|1,0> Homework Equations 3. The Attempt at a Solution We have that |0,1> = ay+ |0,0> I don't...
  8. M

    Electron Clebsch-Gordon coefficients

    Homework Statement The state of an electron is, |Psi> =a|l =2, m=0> ⊗ |up> + Psi =a|l =2, m=1> ⊗ |down>, a and b are constants with |a|2 + |b|2 = 1 choose a and b such that |Psi> is an eigenstate of the following operators: L2, S2, J2 and Jz. The attempt at a solution I am really not sure...
  9. A

    Relabeling spin or angular momentum operators

    Spin or angular momentum in my book is formulated in the basis of eigenstates of the operator that measures the angular momentum along the z-axis. But in principle I guess this could just as well have been done in the basis of eigenstates of Ly or Lx. Will that change anything in the equations...
  10. Pruddy

    Evaluating Operators: ABF(x) and BAF(x)

    Homework Statement Given the operator A = d/dx and B = x and the function f(x) = xe^(-ax) evaluate : ABF(x) and BAF(x) Do these operators commute (yes/No) Homework Equations [A,B]F(x) = ABF - BAF = 0 ; means they commuteThe Attempt at a Solution [A,B]F(x) = ABF - BAF = 0 =d/dx(x^2e^-ax) -...
  11. B

    Tensor Fields - Tensor Product of Two Gradient Operators

    I'm trying to re-derive a result in a paper that I'm struggling with. Here is the problem: I wish to calculate (\nabla \otimes \nabla) h where \nabla is defined as \nabla = \frac{\partial}{\partial r} \hat{\mathbf{r}}+ \frac{1}{r} \frac{\partial}{\partial \psi} \hat{\boldsymbol{\psi}} and...
  12. E

    Adjoint and inverse of product of operators

    I know for two linear operators $$H_1, H_2$$ between finite dimensional spaces (matrices) we have the relations (assuming their adjoints/inverses exist): $$(H_1 H_2)^* = H_2^* H_1^*$$ and $$(H_1 H_2)^{-1} = H_2^{-1} H_1^{-1}$$ but does this extend to operators in infinite dimensions? Thanks.
  13. W

    Is the Quotient of Two Operators AB-1 or B-1A?

    HI, Suppose there are two operators A and B , We have to find A /B - Will it equal to AB-1 OR B-1 A , Because i have read that it equals to AB-1 , BUT i could not find reason for that. thanks
  14. J

    Commutation of squared angular momentum operators

    Hello there. I am trying to proove in a general way that [Lx2,Lz2]=[Ly2,Lz2]=[Lz2,Lx2] But I am a little bit stuck. I've tried to apply the commutator algebra but I'm not geting very far, and by any means near of a general proof. Any help would be greatly appreciated. Thank you.
  15. T

    Lorentz transforming differential operators on scalar fields

    Homework Statement I'm reading Peskin and Schroeder to the best of my ability. Other than a few integration tricks that escaped me I made it through chapter 2 with no trouble, but the beginning of chapter three, "Lorentz Invariance in Wave Equations", has me stumped. They are going through a...
  16. G

    What Defines a Local Operator in Position Space?

    Is it okay to define a local operator as an operator whose matrix elements in position space is a finite sum of delta functions and derivatives of delta functions with constant coefficients? Suppose your operator is M, and the matrix element between two position states is <x|M|y>=M(x,y). It...
  17. D

    Irreducible linear operator is cyclic

    I´m having a hard time proving the next result: Let T:V→V be a linear operator on a finite dimensional vector space V . If T is irreducible then T cyclic. My definitions are: T is an irreducible linear operator iff V and { {\vec 0} } are the only complementary invariant subspaces. T...
  18. S

    Question about spin operators and eigenvalues

    I've been watching Leonard Susskind's videos on quantum entanglements. Naturally, one of the things that he has been discussing is spin and its various operator Hermitian matrices and eigenvalues. Now I have two main questions about this: 1. I know that if you apply a spin operator σ (which is...
  19. P

    Matrix representation of an operator in a new basis

    Homework Statement Let Amn be a matrix representation of some operator A in the basis |φn> and let Unj be a unitary operator that changes the basis |φn> to a new basis |ψj>. I am asked to write down the matrix representation of A in the new basis. Homework EquationsThe Attempt at a Solution...
  20. Ahmad Kishki

    Confusion over quantum mechanics operators

    are operators solely used to find the expectation value of something? What does it mean to use the momentum operator over wavefunction? What does it give? I am guessing it doesn't give momentum since momentum can never be a function of space. How to calculate kinetic energy, given the...
  21. WannabeNewton

    Charge dependence of operators in QED renormalization

    Hi all. Consider a UV cutoff regulator ##\Lambda## with an effective QED lagrangian ##\mathcal{L}_{\Lambda} = \bar{\psi}_{\Lambda}(i\not \partial - m_{\Lambda})\psi_{\Lambda} - \frac{1}{4}(F^{\mu\nu}_{\Lambda})^2 - e_{\Lambda}\bar{\psi}_{\Lambda}\not A_{\Lambda}\psi_{\Lambda}##. One can of...
  22. N

    Simple question concerning Hermitian operators

    Hi. This might sound like a stupid question, but is it, in general, true that ##(\hat{H} \psi)^* \psi'= \psi^* \hat{H}^*\psi'##? Here ##\hat{H}## is a hermitian operator and ## \psi## a wave function. I.e. do they switch places even when not inside an inner product? I am aware of the fact that...
  23. P

    Commuting quantum mechanical operators

    Homework Statement Two Hermitian operators X and Y have a complete set of mutual eigenkets. Show that [X,Y]=0 and interpret this physically. Homework Equations [X,Y]=XY-YX If [X,Y]=0, XY=YX The Attempt at a Solution I have proved that [X,Y]=0, but I'm just falling a little short of...
  24. naima

    Do E and B Commute in Magnetic Field Expressions?

    I know that the electric field can be expressed in term of creation and annihilation operators; Is it the same for the magnetic field B ?
  25. 2

    Question about creation and annihilation operators?

    Hello! I am reading about the creation and annihilation operators and I don't get how you find the creation operator from the annihilation one. The creation one is \hat{a}=\sqrt{\frac{m \omega}{2 \hbar}}\left( \hat{x}+\frac{i \hat{p}}{m \omega}\right) and the annihilation operator is...
  26. J

    Commutation relation for Hermitian operators

    Homework Statement The Hermitian operators \hat{A},\hat{B},\hat{C} satisfy the commutation relation[\hat{A},\hat{B}]=c\hat{C}. Show that c is a purely imaginary number. The Attempt at a Solution I don't usually post questions without some attempt at an answer but I am at a loss here.
  27. DrClaude

    Expectation value of a product of hermitian operators

    I'm trying to derive something which shouldn't be too complicated, but I get different results when doing things symbolically and with actual operators and wave functions. Some help would be appreciated. For the hydrogenic atom, I need to calculate ##\langle \hat{H}\hat{V} \rangle## and...
  28. 2

    Trouble with Hermitian operators?

    I am looking at the derivation of the Heisenberg Uncertainty Principle presented here: http://socrates.berkeley.edu/~jemoore/p137a/uncertaintynotes.pdf and am confused about line (21)... I do not understand why AB and BA are complex conjugates of each other... (I'm still in high school so I...
  29. gonadas91

    Fermionic Operators & Anticommutation: All You Need to Know

    Hi ! I have a doubt about fermionic operators with the anticommutation relations. I know they follow anticommutation, that is, \begin{eqnarray} \lbrace c_{i}^{\dagger},c_{j}\rbrace=\delta_{i,j} \end{eqnarray} That is for fermionic operators. But, suppose I have two different kind of fermionic...
  30. T

    Operators A & B Commute: Explain Why or Why Not?

    Homework Statement Determine whether or not the following pairs of operators commute...and there was one I could not solve...according to the back of the textbook, I do understand 14.c does NOT commute, but I don't understand... (14)c. A = SQR B = SQRT Homework Equations ABf(x) - BAf(x) = 0...
  31. kmm

    Commuting operators require simultaneous eigenfunctions?

    Here is what I understand. The generalized uncertainty principle is: \sigma^{2}_{A} \sigma^{2}_{B} \geq ( \frac{1}{2i} \langle [ \hat{A}, \hat{B} ] \rangle )^2 So if \hat{A} and \hat{B} commute, then the commutator [ \hat{A}, \hat{B} ] = 0 and the operators are compatible. What I don't...
  32. F

    How to Determine the Eigenvalues of a Hermitian Operator?

    Homework Statement I have a hermitian Operator A and a quantum state |Psi>=a|1>+b|2> (so we're an in a two-dim. Hilbert space) In generally, {|1>,|2>} is not the eigenbasis of the operator A. I shall now show that the Eigenvaluse of A are the maximal (minimal) expection values <Psi|A|Psi>.The...
  33. A

    Is Matrix Addition Commutative?

    Suppose we have linear operators A' and B'. We define their sum C'=A'+B' such that C'|v>=(A'+B')|v>=A'|v>+B'|v>. Now we can represent A',B',C' by matrices A,B,C respectively. I have a question about proving that if C'=A'+B', C=A+B holds. The proof is Using the above with Einstein summation...
  34. T

    Quantum mechanics: simultaneous eigenstates for operators

    Homework Statement Suppose that a state |Ψ> is an eigenstate of operator B, with eigenvalue bi. Homework Equations i. What is the expectation value of B? ii. What is the uncertainty of B? iii. Is |Ψi an eigenstate of B2 or not? iv. What is the uncertainty of B2? part B : Suppose, instead...
  35. R

    Missing h-bar in showing SHO in terms of ANHIL and CREA operators is correct

    this is the given: the problem is the middle term, if the h-bar w outside the set brackets is canceled with the h-bar w of the m/2hw, then there will be a h-bar w that is left introduced from the middle term, i.e. i\frac{w}{m}XP- i\frac{w}{m}PX = i\frac{w}{m}[X,P]= i\frac{w}{m}i\hbar but...
  36. L

    Operators on infinite-dimensional Hilbert space

    Hello all! I have the following question with regards to quantum mechanics. If ##H## is a Hilbert space with a countably-infinite orthonormal basis ##\{ \left | n \right \rangle \}_{n \ \in \ \mathbb{N} }##, and two operators ##R## and ##L## on ##H## are defined by their action on the basis...
  37. A

    Matrix Proof using Unitary operators

    Homework Statement Show that if two square matrices of the same rank are related by unitary transformation \hat{A}=\hat{U}^\dagger\hat{B}\hat{U} then their traces and determinants are the same. Homework Equations Tr(\hat{A}) =\sum\limits_{k=0}^{n}a_{kk} \hat{U}^\dagger\hat{U} = 1 The Attempt...
  38. A

    Commuting operators and Direct product spaces

    Under what conditions is the common eigenspace of two commuting hermitian operators isomorphic to the direct product of their individual eigenspaces? As I'm not being able to precisely phrase my doubt, consider this example: Hilbert space of a two dimensional particle is the direct product of...
  39. N

    Why do commuting operators imply that A=A(a) will commute with b?

    Hi. Say a, A(a) and b are well behaving functions. Then say [a,b] = 0, i.e. a and b commute. Why will this automatically mean that A=A(a) will commute with b? Can somebody give me an intuitive explanation, or link me to some proof?
  40. R

    Eigenvalues and operators, step the involves switching and substitutin

    Operator C = I+><-I + I-><+I Wavefunction PSI = Q I+> +V I-> C PSI = Q I-> + V I+> note the I is just a straight line (BRAKET vectors), the next step is where I get confused, p is subbed in and the ket vectors switch places... C PSI = pQ I+> + pV I-> <---- why?? therefore V = pQ and Q =...
  41. S

    Self-adjoint operators and Hermitian operators

    I was wondering what the difference is between the two. Would be nice if someone could explain the difference in simple terms, because it appears to be essential to my quantum mechanics course.
  42. Strilanc

    Translating cumulative rotations into Pauli operators

    I want to write a program that, given the tracked position of a cube being rotated, applies analogous operations to a single qubit. The issue I'm running into is that, although operations correspond to rotations on the Bloch sphere, the mapping isn't one-to-one. So when I try to map back to...
  43. A

    Dependence of operators on the wave function

    in the time-dependent schrodinger equation , our sir told us about energy and momentum operators . He just defined them , the equation was of the form Aexp(i(kx−ωt)) .if we take the equation of the form Aexp(i(kx+ωt)) will those operators change . if so generally for a wave how do we determine...
  44. D

    Linear operators and vector spaces

    Hi all, I've been doing some independent study on vector spaces and have moved on to looking at linear operators, in particular those of the form T:V \rightarrow V. I know that the set of linear transformations \mathcal{L}\left( V,V\right) =\lbrace T:V \rightarrow V \vert \text{T is linear}...
  45. D

    Squared operators and sums of operators in practice

    Consider a one dimensional harmonic oscillator. We have: $$\hat{n} = \hat{a}^{\dagger} \hat{a} = \frac{m \omega}{2 \hbar} \hat{x}^2 + \frac{1}{2 \hbar m \omega} \hat{p}^2 - \frac{1}{2}$$ And: $$\hat{H} = \hbar \omega (\hat{n} + \frac{1}{2})$$ Let's say we want to measure the total...
  46. D

    Linear operators and change of basis

    Following on from a previous post of mine about linear operators, I'm trying to firm up my understanding of changing between bases for a given vector space. For a given vector space V over some scalar field \mathbb{F}, and two basis sets \mathcal{B} = \lbrace\mathbf{e}_{i}\rbrace_{i=1,\ldots ...
  47. D

    MHB Mean and variance of difference operators on a time series process

    \text{Consider the following decomposition of the time series }{Y}_{t}\text{ where }{Y}_{t}={m}_{t}+{\varepsilon}_{t},\text{ where }{\varepsilon}_{t}\text{ is a sequence of i.i.d }\left(0,{\sigma}^{2}\right)\text{ process. Compute the mean and variance of the process }{\nabla}_{2}{Y}_{t}\text{...
  48. lfqm

    Qubits and angular momentum-like operators

    Hi guys, my quesion is quite simple but I think I need to give some background... Let's suppose I have 3 qubits, so the basis of the space is: \left\{{\left |{000}\right>,\left |{001}\right>,\left |{010}\right>,\left |{100}\right>,\left |{011}\right>,\left |{101}\right>,\left...
  49. D

    Linear operators & mappings between vector spaces

    Hi, I'm having a bit of difficulty with the following definition of a linear mapping between two vector spaces: Suppose we have two n-dimensional vector spaces V and W and a set of linearly independent vectors \mathcal{S} = \lbrace \mathbf{v}_{i}\rbrace_{i=1, \ldots , n} which forms a basis...
  50. B

    Dynamical Variables As Operators

    In Quantum Mechanics, why do the dynamical variables become operators? What is the justification or motivation, if any exist?
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