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. R

    What is the meaning of \frac{1}{A}\left|\phi\rangle in quantum mechanics?

    I am led to believe (because it is in a paper I am reading) that \frac{1}{H - z} \left|\phi\rangle = \frac{1}{E - z}\left|\phi\rangle where H is the hamiltonian, \left|\phi\rangle is an energy eigenstate with energy E, and z is a complex variable. In attempting to understand this expression...
  2. K

    How do I convert CC-NOT gates to OR operators?

    Fredkin Gates are supposed to be universal. So far I've gotten AND, OR and NOT out of them but I can't figure out XOR. Any help? I know that A XOR B = (A AND NOT B) OR (B AND NOT A), but trying to recreate that with Fredkin Gates is not very elegant... is that the only way? Edit: I guess I...
  3. Q

    Raising and lowering operators on a simple harmonic oscillator

    Homework Statement Hi, I'm currently studying for a quantum mechanics exam but I am stuck on a line in my notes: Ha\left|\Psi\right\rangle =\hbar\omega\left(a^{t}a a + \frac{a}{2}\right)\left|\Psi\right\rangleHa\left|\Psi\right\rangle =\hbar\omega\left(\left(a a^{t} - 1\right)a +...
  4. M

    Consistency of solutions using operators (Energy ladder)

    Hi, I've been reading about the use of the lowering and raising operators to solve quantum mechanical problems and I have this question in mind. In the book "Introduction to Quantum Mechanics", by David Griffiths, page 35, he notes out that there should be only one energy ladder, so what...
  5. haael

    Fermion annihilation operators from position and momentum

    Is it possible to express fermion annihilation operator as a function of position and momentum? I've seen on Wikipedia the formula for boson annihilation operator: \begin{matrix} a &=& \sqrt{m\omega \over 2\hbar} \left(x + {i \over m \omega} p \right) \\ a^{\dagger} &=& \sqrt{m \omega...
  6. H

    How Do You Calculate the Expectation Value of L_z Using cos(φ)?

    Homework Statement Hi, my problem is with part two of the question I've attached. I'm not exactly sure what they are expecting me to do, is it simply calculating the expectation value of L_z , from the wavefunction given (i.e. cos(φ)) Thanks.
  7. D

    Equation of motion and operators in the interaction picture.

    Homework Statement I have a question that says: What is the equation of motion for a general operator in the interaction picture. I.e. how does the time derivative of the operators behaves ? Show this. And then I have to find the time development for the annihilation and creation operator...
  8. J

    Angular momentum/Hamiltonian operators, magnetic field, basis states problem?

    Hi, Here's my problem, probably not that difficult in reality but I don't get how to approach it, and I've got an exam coming up soon... An atom with total angular momentum l=1 is prepared in an eigenstate of Lx, with an eigenvalue of \hbar. (Lx is the angular momentum operator for the...
  9. T

    Help Finding eigenvalues of angular momentum operators

    urgent help!.. Finding eigenvalues of angular momentum operators the question is asking to find the eigenvalues of: 3/5 Lx - 4/5 Ly ... I feel that i have to connect it with the L^2 and Lz operators but i just have no idea how to start .. any suggestions will be greatly appreciated ..
  10. D

    Problems on quantum field operators in QFT

    Hello! I met some annoying problems on quantum field operators in QFT.They are as follows: (1)The quantum field operator( scalar field operator, for example),is often noted as φ（r,t). Can it be interpreted as like this: φ（r,t) is the coordinate represetation of a...
  11. H

    Expectation value of spin operators.

    Homework Statement If an electron is in an eigen state with eigen vector : [1] [0] what are the expectation values of the operators S_{x}, and S_{z} Interpret answer in terms of the Stern-Gerlach experiment. The Attempt at a Solution Im not too sure how to calculate the...
  12. S

    Polynomial differential operators

    Homework Statement p(D) is a polynomial D operator of degree n>m. Suppose a is a m fold root of p(t)=0, but not a (m+1) fold root. Verify that \frac{1}{p(D)}e^{at}=\frac{1}{p^{(m)}(a)}t^me^{at} where p^{(m)}(t) is the m^{th} derivative of p(t).Homework Equations For this question, we were...
  13. C

    What's the difference between these differential operators?

    I'm learning fluid mechanics, and I am confused about the following differential operators. What's the difference between each?
  14. M

    Diagonal Linear Operator T in L(H): Examples

    I am trying to find an example of a diagonal linear operator T in L(H) H is hilbert space that is bounded but not compact and also one which is compact but not Hilbert-Schmidt. any Ideas?? Where diagonal means Ten=§en where § is the eigenvalue and en is on orthonormal basis.
  15. R

    Differential operators - the rules

    I always get slightly confused with the rules of differentials. now \frac{d^{2}y}{dx^{2}} is the scond derivative of the function y(x but rooting this does NOT give the first derivative dy/dx However, with the operator \frac{d^{2}}{dx^{2}}, it seems that you can root this and it DOES...
  16. D

    Understanding Shankar's Principles of QM: Changing Basis of Operators

    Hi, I'm reading Shankar's Principles of QM and I find it not very clear on how exactly should I change basis of operator. I know how to change basis of a vector so can I treat the columns of operator matrix as vectors and change them? Or is it something else?
  17. N

    Interpreting operators in second quantization

    Hi guys When working with operators in second quantization, I always imagine c^\dagger_ic_j as denoting the "good old" matrix element \left\langle {i} \mathrel{\left | {\vphantom {i j}} \right. \kern-\nulldelimiterspace} {j} \right\rangle . But how should I interpret an...
  18. I

    Story of Operators Creation/Anihilation

    Hi everyone ! Could you tell me who is the inventor of these two operators (creation/anihilation) ? Was he a mathematician ? A physicist ? or both ? Who was the first to use them in Quantum Mechanics ? It's hard to find this kind of information. Thanks Jonathan
  19. 0

    Precedence of logical operators

    based on what is it concluded that this is operation precedes that operation?
  20. N

    How Do You Redefine Grad, Div, and Curl in a New Coordinate System?

    hi all, Simple questions.. I am dealing with the del operator (grad, div curl) in one coord system, but say I parametrise my system into another one. How then do I redefine the grad, div, and curl operators. Any links would be really helpful.
  21. L

    Exchange Operators & Spin Statistics - I don't the conclusions

    Today in class, by the existence of an operator that exchanges the states of two indistinguishable particles, we attempted to derive the existence of fermions and bosons & how this relates to the symmetries of multiparticle wave functions. The argument given in my textbook is: define an...
  22. J

    Linear Algebra with linear operators and rotations

    Definie linear operators S and T on the x-y plane as follows: S rotates each vector 90 degress counter clockwise, and T reflects each vector though the y axis. If ST = S o T and TS = T o S denote the composition of the linear operators, and I is the indentity map which of the following is true...
  23. N

    Expectation Values and Operators

    I've never seen an expectation value taken and would greatly appreciate seeing a step by step of how it is done. Feel free to use any wavefunction, this is the one I've been trying to do: In the case of \Psi=c1\Psi1 + c2\Psi2 + ... + cn\Psin And the operator A(hat) => A(hat)\Psi1 =...
  24. N

    Understanding Ladder Operators

    Calculate [Lz,L+] By defintion ladder operators are: L+=Lx+iLy L-=Lx-iLy Important Relations: LxLy = i\hbarLz, LyLz = i\hbarLx, LzLx = i\hbarLy Lx = ypz - zpy, Ly = xpz - zpx, Lz = xpy - ypx To start solving; [Lz,L+] Lz - (Lx + iLy) = 0 Multiply through by \hbar...
  25. D

    Proving Linearity of Matrix Operators: Is L(A)=2A a Linear Operator?

    L(A)=2A My book doesn't have any examples of how to do this with matrices so I don't know how to approach this.
  26. B

    Linear operators, eigenvalues, diagonal matrices

    So I have a couple of questions in regards to linear operators and their eigenvalues and how it relates to their matrices with respect to some basis. For example, I want to show that given a linear operator T such that T(x_1,x_2,x_3) = (3x_3, 2x_2, x_1) then T can be represented by a diagonal...
  27. P

    Angular Momentum Operator in terms of ladder operators

    Homework Statement http://img716.imageshack.us/i/captur2e.png/ http://img716.imageshack.us/i/captur2e.png/ Homework Equations Stuck on the last part The Attempt at a Solution http://img689.imageshack.us/i/capturevz.png/ http://img689.imageshack.us/i/capturevz.png/
  28. E

    Linear Operators in Hilbert Space - A Dense Question

    Let H be a Hilbert space and let S be the set of linear operators on H. Is there a proper subset of S that is dense in S?
  29. Z

    Can Linear Operators A and B Affect the Rank of AB in V?

    Studying old exam papers from my college I came across the following: Given linear operators A,\,B: V\rightarrow V, show that: \textrm{rk}AB\le \textrm{rk}A My solution: Since all v \in \textrm{Ker}B are also in \textrm{Ker}AB (viz ABv=A(Bv)=A(0)=0) and potentially there are w \in...
  30. E

    How measureable parameters associate with operators

    Homework Statement in quantum mechanics, if we have a wave function, and an operator, we can know the eigenvalue from the eigen equation:\hat{F}\phi=f\phi. but how we obtain the mathematical form of operator \hat{F}? Homework Equations \hat{x} \rightarrow x ? \hat{p} \rightarrow -ih...
  31. H

    Proving an Eigenfunction of Momentum Operators

    Homework Statement Homework Equations Stated in the question. The Attempt at a Solution It is a eigenfunction of L_z as it has no dependence on Z? Not sure if I can just state this, I do need to actually prove it but I can't get the calculations to work. I managed a similar...
  32. P

    Quantum Operators (or just operators in general)

    Homework Statement \phi_1 and \phi_2 are normalized eigenfunctions of observable A which are degenerate, and hence not necessarily orthogonal, if <\phi_1 | \phi_2> = c and c is real, find linear combos of \phi_1 and \phi_2 which are normalized and orthogonal to: a) \phi_1; b) \phi_1+\phi_2...
  33. N

    Where Can I Learn Quantum Mechanics and Understand Linear Operators?

    I'm looking for a good website for understanding Quantum Mechanics (i.e. Time Independent Schrodinger Eq'n, Harmonic Oscillators, Rigid Rotors, etc) The operator is linear if the following is satisfied: A[c*f(x)+d*g(x)]=c*A[f(x)]+d*A[fg(x)], where A = an operator of any kind I'm having...
  34. T

    Understanding Bounded Operators in Quantum Mechanics

    hi. i'm reading "quantum mechanics in hilbert space" and a don't get a basic point for bounded operators. def. 1 a set S in a normed space N is bounded if there is a constant C such that \left\| f \right\| \leq C ~~~~~ \forall f \in S def. 2 a transformation is called bounded if it maps...
  35. D

    Hermitian operator-prove product of operators is Hermitian if they commute

    Hermitian operator--prove product of operators is Hermitian if they commute Homework Statement If A and B are Hermitian operators, prove that their product AB is Hermitian if and only if A and B commute. Homework Equations 1. A is Hermitian if, for any well-behaved functions f and g...
  36. D

    How to Derive the Velocity Operator in Quantum Mechanics?

    Hello! I have a task to do where I do not know where to start or where to find more information. At first, this is just the problem statement: Velocity operator \mathbf{\hat{v}} is defined by the following equations: \frac{d}{dt} \mathbf{\bar{r}} = \left< \psi | \mathbf{\hat{v}} |...
  37. L

    Query regarding Commuting operators

    I am having a problem with a couple of problems involving commutating operators. Homework Statement 1. How do i find the commutation operators of x and ∂/∂x 2. If the angular momenta about 3 rotational axes in a central potential commute then how many quantum numbers we would get? And why...
  38. A

    Exponential of creation/annihilation operators

    Hello! I found on this webpage: http://www-thphys.physics.ox.ac.uk/people/JohnCardy/qft/costate.pdf page 1, on the bottom that e^{\phi^* a } f(a^{\dagger} , a ) = f(a^{\dagger} + \phi^*, a) e^{\phi^* a } I have tried to prove this, writing both as taylor series, but the problem is to...
  39. C

    Commutativity of Differential Operators in Lagrangian Mechanics

    Hello. I am having trouble realizing the following relation holds in Lagrangian Mechanics. It is used frequently in the derivation of the Euler-Lagrange equation but it is never elaborated on fully. I have looked at Goldstein, Hand and Finch, Landau, and Wikipedia and I still can't reason...
  40. H

    Commutator problem with momentum operators

    Homework Statement Find the commutator \left[\hat{p_{x}},\hat{p_{y}}\right] Homework Equations \hat{p_{x}}=\frac{\hbar}{i}\frac{\partial}{\partial x} \hat{p_{y}}=\frac{\hbar}{i}\frac{\partial}{\partial y} The Attempt at a Solution [\hat{p}_{x}...
  41. I

    Raising and lowering operators

    I'm confused about these two forms of the raising/lowering operators for the harmonic oscillator. When each one is used? a_+\psi_n=i\sqrt{(n+1)\hbar\omega} \psi_{n+1} a_-\psi_n=-i\sqrt{n\hbar\omega} \psi_{n-1} a_+|\psi_n\rangle=\sqrt{n+1} |\psi_{n+1}\rangle...
  42. homology

    Is the trace of a linear operator independent of orthonormal basis?

    Hi, I came across a line (http://www.springerlink.com/content/t523l30514754578/) about how the trace of a linear operator is not, in general, independent of the choice of orthonormal basis. The link states that such an operator may have a trace that converges for one basis but not another...
  43. M

    QFT general properties operators

    Hi all, I have quite basic questions about the general properties of operators in quantum field theory. When quantizing the free scalar field, for instance, you promote the classical fields to operators and impose suitable commutation relations (canonical quantization). In momentum space the...
  44. H

    Identifying Self-Adjoint Operators

    Homework Statement If A has eigenvalues 0 and 1, corresponding to the eigenvectors (1,2) and (2, -1), how can one tell in advance that A is self-adjoint and real. Homework Equations e=m^2 The Attempt at a Solution I can show that A is real: it has real orthogonal eigenvectors and...
  45. G

    Ladder Operators acting upon N Ket

    I can't seem to find information regarding this anywhere. I understand why when the ladder operators act upon an energy eigenstate of energy E it produces another eigenstate of energy E \mp\hbar \omega. What I don't understand is why the following is true: \ a \left| \psi _n \right\rangle...
  46. B

    Quantum Mechanics: Infinitesimal Translation Time Evolution Operator

    Two quantum mechanics operators are infinitesimal translation and time evulotion operators.Is there an infinitesimal translation time evolution operator similar to relativistic mechanics?
  47. G

    Hamiltonian being a function of either orbital and spin operators

    Homework Statement The title presents my problem. I know in principle how to find eigenvalues and eigenfunctions of the Hamiltonian if it depends only on orbital operators or in spin operators. On the other hand I have no clue how to solve it if there are both types of operators. The...
  48. G

    Hamiltonian being a function of either orbital and spin operators

    Homework Statement The title presents my problem. I know in principle how to find eigenvalues and eigenfunctions of the Hamiltonian if it depends only on orbital operators or in spin operators. On the other hand I have no clue how to solve it if there are both types of operators. The...
  49. F

    What is the equation for representing a linear operator in terms of a matrix?

    I'm working through a proof that every linear operator, A, can be represented by a matrix, A_{ij}. So far I've got which is fine. Then it says that A(\textbf{e}_{i}) is a vector, given by: A(e_{i}) = \sum_{j}A_{j}(p_{i})e_{j} = \sum_{j}A_{ji}e_{j}. The fact that its a vector is fine...
  50. V

    A question on eigenstates and operators

    Why can we say that: <x'|e^{i\hat{x}}|x>=e^{ix'}\delta(x'-x) where where \hat{x} is an operator? I mean if \hat{x}|x>=x|x> we may write <x'|\hat{x}|x>=x<x'|x>=x\delta(x'-x) but in the expression at the top, we have an exponential operator (something I've never come across...
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