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. N

    Understanding the Thermal Average of Operators in Quantum Mechanics

    Hi Please take a look at equation 8.60 in the following link...
  2. C

    How do we make sense of exponentiating an operator in quantum mechanics?

    Most quantum textbooks will tell you that converting between the Schrödinger and Heisenberg pictures involves something like the following: |\Psi(t)\rangle = e^{i\hat{H}(t-t_0)}|\Psi(t_0)\rangle This does make sense to me conceptually: we define eigenstates of the Hamiltonian |E\rangle, where...
  3. N

    Commute Operators: Hi Niles - Find Out Now

    Hi Say I have the creation/annihilation operators for fermions given by c and the exponential operator exp(-iHt), where H denotes the Hamiltonian of the (unperturbed) system. Is there any way for me to find out if exp(-iHt) and c (and its adjoint) commute?Niles.
  4. P

    Exploring K-Space: Homework Equations in Bose Operators

    Homework Statement How this would look in K space -\sum_{\vec{n},\vec{m}}I_{\vec{n},\vec{m}}\hat{a}^+_{\vec{n}}\hat{a}_{\vec{n}}\langle \hat{a}^+_{\vec{n}}\hat{b}^+_{\vec{m}}\rangle I need to get -\sum_{\vec{k}}\hat{a}^+_{\vec{n}}\hat{a}_{\vec{n}}\frac{1}{N}\sum_{\vec{q}}J(\vec{q})\langle...
  5. B

    Understanding Degenerate Eigenvalues and Vectors in Math Operations

    Homework Statement please see attached Homework Equations The Attempt at a Solution Ok so I've done A and have worked out eigenvalues and vectors of H and B For H I get 4 possible eigenvectors (1,0,0) (0,1,1) (0,0,1) and (0,1,0) . The q is why does neither matrix uniquely...
  6. I

    An identity for functions of operators

    Is there an easy way to prove the identities: e^{\hat{A}}e^{\hat{B}}=e^{\hat{A}+\hat{B}}e^{[\hat{A},\hat{B}]/2} and e^{\hat{A}}\hat{B}e^{-\hat{A}}=\hat{B}+[\hat{A},\hat{B}]+\frac{1}{2!}[\hat{A},[\hat{A},\hat{B}]]+\frac{1}{3!}[\hat{A},[\hat{A},[\hat{A},\hat{B}]]]+...In Zettili they give that...
  7. S

    Annihilation Operators: Prove af(a^\dagger)|n>=df(a^\dagger)/da|0>

    So we all know about a and a^\dagger. My problem says that if f(a^\dagger) is an arbitrary polynomial in a^\dagger then af(a^\dagger)|n> = \frac{df(a^\dagger)}{da}|0> where |0> is the ground state energy. How can I go about proving this? A hint would be highly appreciated. Thanks,
  8. L

    Find Momentum Operators for 1s Electron in Hydrogen Atom

    Find < px >,< p > and < p2 > for the 1s electron ofa hydrogen atom. i am tried the solution but momentum operators Differential for x or y or z and the wave equation depends on the r !
  9. R

    Correlations between QM operators

    In thermodynamics, two variables A and B are uncorrelated when: <AB>=<A><B> where <> are the expectation values in thermodynamics (for example calculated using Boltzmann distributions). What are the conditions in quantum mechanics for two operators to be uncorrelated, i.e...
  10. E

    What does simultaneous reality and non-commuting operators mean?

    "if Quantum Mechanics (QM) is complete (and there are no "hidden variables"), then there cannot be simultaneous reality to non-commuting operators" - Taken from http://drchinese.com/David/Bell_Theorem_Negative_Probabilities.htm I am trying to understand this sentence but I do not fully...
  11. P

    How to Derive the Inverse of the Sum of Two Operators?

    Hi, I am trying to show that for two operators S and P: (S+P)^{-1}=S^{-1}-S^{-1}P(S+P)^{-1} I can't get anywhere and searching on google I am not even sure if it is possible to solve the general case but the question gives no more hints. Any help appreciated. Thanks. J.
  12. H

    Why do we have to use operators in QM?

    Why do we have to use operators in QM?
  13. C

    Shape Operators and Eigenvalues

    This is probably falls within a problem of Mathematica as opposed to a question on here but I have a question about the following: Given some cylinder with the shape operator matrix: {{0,0},{0,-1/r}} We get eigenvalues 0 and -1/r and thus eigenvectors {0, -1/r} and {1/r, 0} by my...
  14. U

    Why does this Bra Ket (with creation and annihilation operators) equal zero?

    1. Explain why <n|(a-a+)^3|n> must be zero 2. a and a+ (a dagger) are the raising and lowering operators (creation and annihilation operators). 3. Because it says explain, I am not sure any mathematical proof is needed. I am best answer is that because (ignoring that the bracket...
  15. R

    Pervasiveness of linear operators

    Obviously linear operators are ideal to work with. But is there a deeper reason explaining why they're ubiquitous in quantum mechanics? Or is it just because we've constructed operators to be linear to make life easier?
  16. fluidistic

    Commutator, operators momentum and position

    Homework Statement I must calculate [X,P].Homework Equations Not sure. What I've researched through the Internet suggests that [\hat A, \hat B]=\hat A \hat B - \hat B \hat A and that [\hat A, \hat B]=-[\hat B, \hat A]. Furthermore if the operators commute, then [\hat A, \hat B]=0 obviously...
  17. M

    Particle in a box: commuting energy and momentum operators

    Hi, I've been thinking about the following: In an infinitely deep box a particle's energy operator can be written as E = p^2/2m, and the momentum operator as p = -i hbar dx. (particle moves in x direction) I can see that the commutator of E and p is 0, so the operators commute, and should...
  18. D

    Momentum Operators and the Schwartz Integrability Condition

    Hi All, When computing the commutator \left[x,p_{y}\right], I eventually arrived (as expected) at \hbar^{2}\left(\frac{\partial}{\partial y}\left(\frac{\partial f}{\partial x}\right) - \frac{\partial}{\partial x}\left(\frac{\partial f}{\partial y}\right)\right) and I realized that, as correct...
  19. Seanskahn

    Uncertainty Operators in Nouredine Zettili's Book

    Hello community. My second stupid question. In the book by Nouredine Zettili , the uncertaintie operators are defined as \DeltaA = A - <A>, where A is an operator, and <A> = <\psi|A|\psi> , with repect to a normalized state vector |\psi> i was wondering, why is not the uncertainty...
  20. T

    Quantum Mechanics Operators, Hermitian and Eigenvalues

    1. a) The action of the parity operator, \Pi(hat), is defined as follows: \Pi(hat) f(x) = f(-x) i) Show that the set of all even functions, {en(x)}, are degenerate eigenfunctions of the parity operator. What is their degenerate eigenvalue? The same is true for the set of all odd functions...
  21. B

    Unitary operators preserve normalization in arbitrary basis

    Homework Statement To test my knowledge of Sakurai, I asked myself to: "Prove that an operator being unitary is independent of basis." The Attempt at a Solution I want to show the expansion coefficients’ squared magnitudes sum to unity at time “t”, given that they do at time t = t0...
  22. P

    Equations with multiple absolute value operators

    Hello there. I'm having some problems with absolute values when they contain multiple "abs" operators and some other numbers outside the "abs"-es. For example: \left | x+2 \right | - \left | x \right | > 1 If i check it for the positive scenario, the result is true for all x-es. x+2...
  23. M

    Angular momentum operators in quantum mechanics

    Homework Statement H=(J1^2+J2^2)2A+J3^2/2B where J1,2,3 are the angular momentum operators and A and B are just numbers Homework Equations The Attempt at a Solution I rewrote the Hamiltonian as (J^2-Jz^2)/2A + J3^2/2B and got the eigenvalues to be (h^2L(l+1)-h^2m^2)/2A+h^2m^2/2B...
  24. pellman

    Chain rule for functions of operators?

    This is strictly a math question but I figured that since it is something which would show up in QM, the quantum folks might be already familiar with it. Suppose we have an operator valued function A(x) of a real parameter x and another function f, both of which have well defined derivatives...
  25. D

    On commuting of position and momentum operators

    Homework Statement I have to proove: [\hat{y},\hat{p}_y]=[\hat{z},\hat{p}_z]=i\hbar\hat{I} Homework Equations [\hat{A},\hat{B}]=\hat{A}\hat{B}-\hat{B}\hat{A} The Attempt at a Solution Ok so I know that...
  26. J

    Proof that commuting operators have a shared base of eigenfunctions

    I have been told that if we have two operators, A and B, such that AB = BA then this is equivalent with that A and B have a common base of eigenfunctions. However, the proof given was made under the assumption that the operators had a non-degenerate spectrum. Now I understand that one rather...
  27. A

    Linear Operators: Identifying and Solving

    Homework Statement I have some operators, and need to figure out which ones are Linear (or not). For example: 1. \hat{A} \psi(x) \equiv \psi(x+1) Homework Equations I have defined the Linear Operator: \hat{A}[p\psi_{1}+q\psi_{2}]=p\hat{A}\psi_{1}+q\hat{A}\psi_{2} The Attempt at a...
  28. A

    Hermitian Operators: Identifying & Solving Examples

    Homework Statement I have some operators, and need to figure out which ones are Hermitian (or not). For example: 1. \hat{A} \psi(x) \equiv exp(ix) \psi(x) Homework Equations I have defined the Hermitian Operator: A_{ab} \equiv A_{ba}^{*} The Attempt at a Solution I just don't know where...
  29. K

    Is \(x^k p_x^m\) Hermitian?

    Homework Statement Show that the operator x^kp_x^m is not hermitian, whereas \frac{x^kp_x^m+p_x^mx^k}{2} is, where k and m are positive integers. The Attempt at a Solution Is this valid? <x^kp_x^m>^*=\left(\int_{-\infty}^\infty\Psi^*x^k(-i\hbar)^m\frac{\partial^m\Psi}{\partial...
  30. K

    Does it make sense to define operators like r,theta, phi

    I'm pondering, since we've introduced formalism, all operators are either scalars or vector components, does it make sense to define operators like r, theta, phi (as in spherical coordinates) which are neither? In classical mechanics we can easily transform observables fro cartesian to...
  31. A

    If two operators commute (eigenvector question)

    Suppose \Omega_1 and \Omega_2 satisfy [\Omega_1,\Omega_2]=0 and \Omega = \Omega_1 + \Omega_2. If \Psi_1 and \Psi_2 are eigenvectors of \Omega_1 and \Omega_2, respectively, don't we know that the (tensor?) product \Psi = \Psi_1 \Psi_2 is an eigenvector of \Omega? Also, if the \Psi_i are...
  32. D

    Fermion creation and annihilation operators

    Hi. If c and c^\dagger are fermion annihilation and creation operators, respectively, we know that cc^\dagger+c^\dagger c=1 and cc=0 and c^\dagger c^\dagger=0. I can use this to show the following [c^\dagger c,c]=c^\dagger cc-c c^\dagger c=-cc^\dagger c=-c(1-cc^\dagger)=-c But on the...
  33. T

    Quantum harmonic oscillator: ladder operators

    Homework Statement For a particle of mass m moving in the potential V(x) = \frac{1}{2}m\omega^2x^2 (i.e. a harmonic oscillator), it is often convenient to express the position and momentum operators in terms of the ladder operators a_{\pm}: x = \sqrt{\frac{\hbar}{2m\omega}}(a_+ + a_-) p =...
  34. K

    What Is the Position Operator if Momentum Is Given by a Specific Operator?

    Homework Statement Find the operator for position x if the operator for momentum p is taken to be \left(\hbar/2m\right)^{1/2}\left(A + B\right), with \left[A,B\right] = 1 and all other commutators zero. Homework Equations Canonical commutation relation \left [ \hat{ x }, \hat{ p } \right ] =...
  35. P

    Spectrum of angular momentum operators

    Homework Statement I am trying to understand the allowed eigenvalues for the angular momentum operators J and L. In particular why, mj can take integer and half-integer values whereas ml can take only integer values. Homework Equations I have learned about angular momentum operators as...
  36. S

    Density Operators, Trace and Partial Trace

    I have some math questions about quantum theory that have been bugging me for a while, and I haven't found a suitable answer in my own resources. I'll start with the Trace operation. Question A) My understanding is that if we take system A and perform the partial trace over system B, we...
  37. E

    Question Regarding Commutator of two incompatible Hermitian Operators

    I have two questions that are based on the following example involving the Hermitian operator i[A,B]=iAB-iBA for the case of a plane polarized photon. The observable (Hermitian Matrix) for the plane polarized photon, which Professor Susskind gave in his quantum mechanics lecture, lecture...
  38. I

    Comp Sci Help evaluating boolean number and arithmetic operators C++

    Homework Statement !( ((count<10) || (x<y)) && (count >=0) ) where count is equal to 0Homework Equations i don't think any equations here are necessary except maybe the precedence lawThe Attempt at a Solution they combined 'and' and 'or' which confused the heck out of me. How do i figure out...
  39. R

    Vanishing commutator for spacelike-separated operators?

    In David Tong's QFT notes (http://www.damtp.cam.ac.uk/user/tong/qft/qft.pdf p. 43, eqn. 2.89) he shows how the commutator of a scalar field \phi(x) and \phi(y) vanishes for spacelike-separated 4-vectors x and y, establishing that the theory is causal. For equal time, x^0=y^0, the commutator is...
  40. B

    Computing Scalar Product in Antisymmetric Fock Space w/ Creator Operators

    We use the antisymmetric Fock space ( "fermions"). We denote by c(h) a creator operator. I need to evaluate the following quantity: < \Omega , \big(c(h_1)+c(h_1)^{*}\big)\big(c(h_2)+c(h_2)^{*}\big) \ldots \big(c(h_n)+c(h_n)^*\big)\Omega> where \Omega is the unit vector called vaccum...
  41. J

    Wondering about operators and matrix representations?

    Hi, this isn't a homework question per se (it's the summer hols, I'm between semesters) but it's something that I never really got during the QM module I just did. I found myself blindly calculating exam & homework problems, and just feel like this is some stuff I should get cleared up...
  42. M

    Commutation relation of operators

    Im reading in a quantum mechanics book and need help to show the following relationship, (please show all the steps): If A,B,C are operators: [A,BC] = B[A,C] + [A,B]C
  43. C

    Solving Commuting Operator Equations: Understanding Lz and T in Atoms

    Hi there, I'm neither a physicist or a mathematician, so I'm having a bit of trouble understanding commutative properties of operators. Here is an example question, if anyone could help show me how to solve it, it would be greatly appreciated. Show that Lz commutes with T and rationalize...
  44. J

    Physical interpretation of operators in QM?

    hi, I am a novice to quantum mechanics and get a lot of troubles with operators. I cannot explain why: - why QM uses operators for observables such as position, momentum, energy, ..ect, but classical physics does not? - what are physical interpretations of operators? - why are operators needed...
  45. L

    Compact Operators on a Hilbert Space

    Hello, I hope I am asking this in the right area of the forums. My teacher wrote the following formula down at our last meeting, and I was wondering if it was true ( \mathcal{H} is the infinite dimension separable Hilbert space): \mathcal{K} (\mathcal{H}) \approx \mathcal{K} (\mathcal{H}...
  46. L

    Compact Operators on a Hilbert Space

    Hello, I hope I am asking this in the right area of the forums. I wanted to ask if the following formula is true (assuming H is infinite dimensional and separable): \mathcal{K} (\mathcal{H}) \approx \mathcal{K} (\mathcal{H} \oplus \mathcal{H} \oplus \mathcal{H} \oplus \mathcal{H})\approx...
  47. Z

    Quantum Mechanics Operators question

    Homework Statement The operator Q obeys the commutation relation [Q, H] = EoQ, where Eo is a constant with units of energy. Show that if ψ(x) is a solution of the time-independent Schrodinger equation with energy E, then Qψ(x) is also a solution of the time-independent Schrodinger equation...
  48. N

    Do Fermionic Creation and Annihilation Operators Commute?

    Hi guys The fermionic creating and annihiliations operators: Do they satisfy c_{i,\sigma }^\dag c_{i,\sigma }^{} = - c_{i,\sigma }^{} c_{i,\sigma }^\dag for some quantum number i and spin σ, i.e. do they commute?
  49. R

    Show that a group of operators generates a Lie algebra

    Hello there! Above is a problem that has to do with Lie Theory. Here it is: The operators P_{i},J,T (i,j=1,2) satisfy the following permutation relations: [J,P_{i}]= \epsilon_{ij}P_{ij},[P_{i},P_{j}]= \epsilon_{ij}T, [J,T]=[P_{i},T]=0 Show that these operators generate a Lie algebra. Is that...
  50. Simfish

    QM: Sum of projection operators = identity operator?

    Homework Statement So we have an observable K = \begin{bmatrix} 0 & -i \\ -i & 0 \end{bmatrix} and its eigenvectors are v1 = (-i, 1)T and v2 = (i, 1)T corresponding to eigenvalues 1 and -1, respectively. Now if we take the outer products, we get these... |1><1| = (-i, 1)T*(i, 1) =...
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