What is Operators: Definition and 1000 Discussions

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. Y

    Properties of Hermitian Operators: Show Real Expectation Value & Commutativity

    I have some questions about the properties of a Hermitian Operators. 1) Show that the expectaion value of a Hermitian Operator is real. 2) Show that even though \hat{}Q and \hat{}R are Hermitian, \hat{}Q\hat{}R is only hermitian if [\hat{}Q,\hat{}R]=0 Homework Equations The...
  2. B

    Fourier Transform of Hermitian Operators

    Question: Is the Fourier Transform of a Hermitian operator also Hermitian? In the case of the density operator it would seem that it is not the case: \rho(\mathbf{r}) = \sum_{i=1}^N \delta(\mathbf{r}-\mathbf{r}_i) \rho_k = \sum_{i=1}^N e^{-i\mathbf{k} \cdot \mathbf{r}} I have a hard...
  3. F

    Parity Operator, Symmetric Potential: Is V=PV?

    Let's say we have a symmetric potential, in position representation V(x)=V(-x) and let P be the parity operator. Then quite clearly PV=VP but I was told the stronger statement V=PV is not true, but I thought V=\int_{-\infty}^{\infty} V\left|x\right\rangle\left\langle x \right| dx (where I...
  4. F

    Orthonormal basis and operators

    I hope this is the forum to ask this question. We all know that the eigenvectors of a Hermitian operator form an orthonormal basis. But is the opposite true as well. Are the vectors of an orthonormal basis always the eigenvectors of some Hermitian operator? Or do we need added restrictions to...
  5. M

    Angular Momentum Ladder Operators

    I thought that I had angular momentum very well understood, but something has been giving me problems recently. It is often stated in textbooks and webpages alike, that the angular momentum ladder operators defined as J_{\pm} \equiv J_x \pm i J_y Then the texts often go on to say that these...
  6. S

    Product rule for derivatives of operators

    I ve been trying to derive this for some time now. The rule is similar to the one for simple math derivatives. d/dx(A^B^)=dA^/dx B^ + A^ dB^/dx Is the derivation on similar lines. Any directions??
  7. S

    Are there any operators that are not linear?

    Homework Statement Consider the following operators a) Reflection: \hat{I}\Psi(x)=\Psi(-x) , x\in(-\infty,\infty) b) Translation: \hat{T_{a}}\Psi(x)=\Psi(x+a), x\in(-\infty,\infty) c) \hat{M_{c}}: \hat{M_{c}}\Psi(x) = \sqrt{c}\Psi(x) d) \hat{c}\Psi(x)= (\Psi(x))^* e)...
  8. K

    QM: translation and rotation operators : what's the point?

    Homework Statement I understand, mathematically, that the translation operator (both for infinitesimal and finite translations) can be written as a function of the momentum operator. It is said then that momentum "generates" translation. Similiary, the rotation operator can be written as a...
  9. N

    Noncommuting operators and uncertainty relations

    Hello all, I've been thinking about the connection between commutativity of operators and uncertainty. I've convinced myself that to have simultaneous eigenstates is a necessary and sufficient condition for two observeables to be measured simultaneously and accurately. It's also clear...
  10. B

    Commutativity Equation Of Hamilton and Position Operators

    How can we show \left[\hat{H},\hat{x}\right]=\frac{-i\hbar}{m} \hat{p_{x}} ?
  11. T

    Solve Hermitian Operators: Prove Int. w/ Wavefuncs

    Homework Statement Show that if \Omega is an hermitian operator, and \varphi and \psi are (acceptable) wavefunctions, then then \int \phi^{*} \Omega \psi dz = \int \psi (\Omega \phi)^{*} dz Homework Equations Consider the wave function \Psi = \phi + \lambda\psi The Attempt at a...
  12. D

    Understanding the Relationship between Hamilton and Momentum Operators

    why i\hbar(\partial/\partialt+i\Omega)=i\hbarexp(-i\Omegat)\partial/\partialtexp(i\Omegat)
  13. A

    Commutation Relations and Unitary Operators

    I have a problem with deriving another result. Sorry I am new to this field. Please see the attached PDF - everything is there.
  14. A

    Unitary Operators and Lorentz Transformations

    Homework Statement I am trying to learn from Srednicki's QFT book. I am in chapter 2 stuck in problem 2 and 3. This is mainly because I don't know what the unitary operator does - what the details are. Starting from: U(\Lambda)^{-1}U(\Lambda')U(\Lambda)=U(\Lambda^{-1}\Lambda'\Lambda) How does...
  15. E

    Spin angular momentum operators

    I posted this is in the QM section but maybe here would have been better. I don't think it is a hard question for anyone who knows QM: https://www.physicsforums.com/showthread.php?t=181220
  16. E

    Spin angular momentum operators

    The context of this question is chemistry but I think that it contains enough quantum mechanics to warrent posting it here instead of in the chemistry forum. Go to section 2.1.1 at the following site: http://tesla.ccrc.uga.edu/publications/papers/qrevbiophys_v33p371.pdf I am confused...
  17. N

    Ladder Operators: Why, What & Why?

    Why must the ladder operators be \sqrt{\dfrac{m\omega}{2\hbar}}(x+\dfrac{ip}{m\omega}) and \sqrt{\dfrac{m\omega}{2\hbar}}(x-\dfrac{ip}{m\omega})? What is the method that obtain them from schrodinger Equation? And why we know that they are creation and anihilation operator?
  18. C

    What is the Physical Significance of Curl and Div Operators in Physics?

    i am having trouble with understanding the physical significance of these two operators.
  19. marcus

    Dittrich and Thiemann challenge discreteness of LQG area etc operators

    This is very exciting. I have wondered about this merely as a spectator, because e.g. AFAIK the spinfoam formalism has not confirmed that about the geometric operators. What they say is that discrete spectrum HAS NOT BEEN PROVEN yet for the geometric operators, so it could go either way. Also I...
  20. A

    Operators in quantum mechanics

    I'm a newcomer here... so I introduce myself: I've just completed my BS in physics and joining M.Sc... I've interested to take specialisation in Quantum mechanics and will continue in theoretical physics in the future... I'm facing problems understanding the algebra of operators...
  21. K

    Pseudo differential operators

    let be the operator involving an infinite-dimensional ODE f( \partial _{x}) y(x)=h(x) then if h(x)=0 i make the ansatz y(x)=e^{ax} so \sum_{\rho } e^{x\rho} f(\rho) =0 for h(x) different from '0' we construct an orthonormal basis with the solutions given above to give an...
  22. A

    Questions about operators in QM

    helow guys i am atif elahi from pakistan i have some problem in topic operators in quantum mechanics can you people help me i shall be very thankful to you thanks
  23. M

    How does the operator in Bra-Ket notation work in the position basis?

    I'm reading an article where there are an atom with two states, let's call them |0> and |1>. Then the writer defines an operator by |0><1| I know how this operator works in the bra ket notaion, but how does it work, if I want to use it in the position basis? Someone told me that I just...
  24. B

    Operators and Complete State Descriptions in Quantum Mechanics

    What for do we need operators in QM. Where is the complete state description of a quantum object?
  25. R

    A question on bounded linear operators (Functional Analysis)

    Suppose T: X -> Y and S: Y -> Z , X,Y,Z normed spaces , are bounded linear operators. Is there an example where T and S are not the zero operators but SoT (composition) is the zero operator?
  26. M

    Harmonic Oscillator, Ladder Operators, and Dirac notation

    Defining the state | \alpha > such that: | \alpha > = Ce^{\alpha {\hat{a}}^{\dagger}} | 0 >\ ,\ C \in \mathbf{R};\ \alpha \in \mathbf{C}; Now, | \alpha > is an eigenstate of the lowering operator \hat{a}, isn't it? In other words, the statement that \hat{a} | \alpha >\ =\ \alpha | \alpha >...
  27. R

    Unitary Operators: Why is Spectrum on Unit Circle?

    Homework Statement why is the spectrum of the unitary operator the unit circle? Homework Equations i know that U^(-1)=U* and i know this makes U normal i also know that normal means UU*=U*U The Attempt at a Solution i know that from spectral theory there is some lambda in the...
  28. R

    Proving the Nilpotency of Square Triangular Matrices with Zero Diagonal Entries

    Homework Statement Prove that any square triangular matrix with each diagonal entry equal to zero is nilpotent The Attempt at a Solution Drawing out the matrix and multiplying seems a little tedious. Perhaps there is a better way? Is there another way to do this without assuming that the...
  29. N

    Hermite functions,Ladder operators

    Homework Statement It is possibly not a homework problem.However,to do a homework problem,I require this: Boas writes the effect of Ladder operators on y_n that satisfies y"_n-x^2y_n=-(2n+1)y_n,n=0,1,2,3... (D-x)(D+x)y_n=-2ny_n (D+x)(D-x)y_n=-2(n+1)y_n Then,she proved...
  30. D

    Field operators in canonically transformed representations of the CCRs

    Here's a question about inequivalent representations of the CCRs... For a given Hilbert space representation, what is it that determines which set of field operators \phi(x), or \phi(f) if we want to get rigorous a la Wightman, gives us THE field operators for that representation. For example...
  31. M

    Connection coefficients entering differential operators

    I have worked out how the connection coefficients enter into the expression for the Laplacian, for example, in different coordinate systems. Does anyone have general expressions for how the coefficients enter into other expressions such as divergence and curl and grad and so on? Thanks in...
  32. S

    Some questions about reducible matrices and operators

    Hello , This is regarding the equality of nullity between A and PAP(inverse). If my understanding is correct then the thing should be according to the diagram belowV---------------->R1(isomorphic to V) | | | | \/ \/...
  33. A

    Quantum Mechanics Adjoint Operators

    If we have two linear operators A, and B, where A+ is the adjoint of A, how do we prove the property, (AB)+=(B+)(A+)
  34. radou

    Linear independency of operators

    OK, I stumbled upon a problem, but I feel somehow stupid about writing the exact problem down, so I'll ask a more "general" question. I have to see if three linear operators A, B and C from the vector space of all linear operators from R^2 to R^3 are linearly independent. The mappings are all...
  35. A

    Composite Hilbert Spaces and Operators

    So, say I have a composite hilbert space H = H_A \otimes H_B, can I write any operator in H as U_A \otimes U_B? Thanks
  36. S

    Hermitian Operators: Meaning & Showing Properties

    1.What does it mean for an operator to be hermitian? Note: the dagger is represented by a ' 2. How do I show that for any operator ie/ O' that O + O' , i(O-O') and OO' are hermitian? Thanks in advanced
  37. S

    QM: Ladder Operators Explained Step-by-Step

    I am taking a QM course and we are using griffiths intro to QM text, 2nd edition. I like the text but I find it lacking when it comes to explaining ladder operators. I need to see how to use them in a very detailed step-by-step problem. Does anyone know of any good textbooks or websites that...
  38. E

    Matrix representation of ladder operators

    Homework Statement Find the matrices which represent the following ladder operators a+,a_, and a+a- All of these operators are supposed to operate on Hilbert space, and be represented by m*n matrices. Homework Equations a+=1/square root(2hmw)*(-ip+mwx) a_=1/square root(2hmw)*(ip+mwx)...
  39. L

    Solving Operators and Ordering in 3D Electron Energies

    In my question I have to find what the commutation of a electrons kinetic and potentials energys are, in 3 Dimensions. I have started by finding the kinetic operator T and the potential energy from coloumbs law. I have then applied commutation brackets and I'm at the stage where I'm solving the...
  40. U

    Proof of Hermiticity of Adjoint Operators

    Homework Statement A is a non-Hermitian operator. Show that i(A-A^t) is a Hermitian operator.Homework Equations \int \psi_1^*\L\psi_2 d\tau=\int (\L\psi_1)^*\psi_2 d\tau \int \psi_1^*A^t\psi_2 d\tau=\int (A\psi_1)^*\psi_2 d\tauThe Attempt at a Solution \int \psi_1^*i(A-A^t)\psi_2 d\tau =\int...
  41. U

    Hermitian Operators in quantum mechanics

    Homework Statement Within the framework of quantum mechanics, show that the following are Hermitian operators: a) p=-i\hbar\bigtriangledown b) L=-i\hbar r\times\bigtriangledown Hint: In Cartesian form L is a linear combination of noncommuting Hermitian operators. Homework Equations...
  42. N

    Commutation relation of the position and momentum operators

    Homework Statement I've just initiated a self-study on quantum mechanics and am in need of a little help. The position and momentum operators do not commute. According to my book which attemps to demonstrate this property, (1) \hat{p} \hat{x} \psi = \hat{p} x \psi = -i \hbar...
  43. quasar987

    Standard Basis and Ladder operators

    Cohen-Tanoudji defines a "standard basis" of the state space as an orthonormal basis {|k,j,m>} composed of eigenvectors common to J² and J_z such that the action of J_± on the basis vectors is given by J_{\pm}|k,j,m>=\hbar\sqrt{j(j+1)-m(m\pm 1)}|k,j,m\pm 1> But isn't is automatic that such...
  44. R

    What is physical meaning of anticommuting, not anticommuting operators

    hello everyone, while studying QM you learn the physical meaning of commutating operators, namely they have simultaneous eigenstates. For observables it means, that they can be simultaneusly exactly mesured. What is the physical meaning of anticommuting and not anticommuting operators...
  45. B

    Quantum Mechanics - Commuting Operators (very quick question)

    Just a quickie: If two operators commute, what can be said about their eigenfunctions? The only thing I can glem from the chapter in my textbook about this is that the eigenfunctions are equal? Is this right, or have I misread it?
  46. lemma28

    Help with expected value of non-hermitian operators

    I know that with an Hermitian operator the expectation value can be found by calculating the (relative) probabilities of each eigenvalue: square modulus of the projection of the state-vector along the corresponding eigenvector. The normalization of these values give the absolute probabilities...
  47. Reshma

    General Uncertainty Relation between 2 operators

    The general uncertainty relation between two observables A and B. (\Delta A)^2(\Detla B)^2 \geq -{1\over 4}<[A, B]>^2 I have to prove the above relation using the definition of expection values etc. The reference I use (Liboff) have this relation given as an exercise. But Gasiorowicz's book...
  48. A

    Angular Momentum Operators

    Homework Statement Show that for the eigenstate |l,m> of L^2 and Lz, the expectation values of Lx^2 and Ly^2 are <Lx^2>=<Ly^2>=1/2*[l(l+1)-m^2]hbar^2 and for uncertainties, show that deltaLx=deltaLy={1/2*[l(l+1)-m^2]hbar^2}^(0.5) Homework Equations eigenvalues of L^2 are l(l+1)hbar^@...
  49. K

    Is the K-G Operator of the Kelin-Gordon Equation a Time Ordered Function?

    Let be the Kelin-gordon equation (m=0) with a potential so: (-\frac{\partial ^{2}}{\partial t^{2}}+V(x) )\Phi=0 my question is if you consider the wave function above as an operator..is the K-G operator of the form: <0|T(\Phi(x)\Phi(x')|0> T=time ordered I think that in both...
  50. K

    QM having difficulty on proofs of operators

    I know this is a simple part of Quantum Mechanics, but I seem to be having trouble with it, I'm not sure if my math is just wrong or if I'm applying it wrong. The questions that I have are: Prove the following for arbitrary operators A,B and C: (hint-no tricks, just write them out in...
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