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.
A. I can show that A is either hermitian or antihermitian by
$$(B^\dagger B=1-A^2)^\dagger$$
$$B^\dagger B=1-A^\dagger A^\dagger$$
comparing, we know that
$$A^\dagger = \pm A$$
I don't know how I can make use of the communtation relation to get hermiticity of B. But I know that A and B must have...
I know the way to solve the first part is to find <ψ|Αψ> and compare it with <ψΑ|ψ>. This comparison can be done through an integral representation where we take ψ* and act A on ψ to be the integrand, or act A on ψ* and multiply by ψ for the integrand. If the integrals are the same, then the...
Hi
I just wanted to check my understanding of something which has come up when first studying path integrals in QM. If x and px are operators then [ x , px ] = iħ but if x and px operate on states to produce eigenvalues then the eigenvalues x and px commute because they are just numbers. Is...
Suppose Q=2x+t and x=t2, then ∂Q/∂t=1.
But Q can also be written as Q=x+t2+t, then ∂Q/∂t=2t+1.
We now have 2 different answers. But I think there can only be one correct answer.
In reference to the equation in the image, no matter we write Q=2x+t or Q=x+t2+t, <Q> should be the same, so the LHS...
For two quantum oscillators, I have raising and lowering operators and , and the number operator . I need to check if operators below follow commutation relations.
Now as far as I know, SU(2) algebra commutation relation is [T_1, T_2] = i ε^ijk T_3. So, should I just get T_1 and T_2 in...
Hi
If A is a linear operator but not Hermitian then the expectation value of A2 is written as < ψ | A2| ψ >. Now if i write A2 as AA then i have seen the expectation value written as < ψ | A+A| ψ > but if i only apply the operators to the ket , then could i not write it as < ψ | AA | ψ > ? In...
Hey all,
I saw a formula in this paper: (https://arxiv.org/pdf/physics/0011069.pdf), specifically equation (22):
and wanted to know if anyone knew how to derive it. It doesn't seem like a simple application of BCH to me.
Thanks.
Here again with another question about the Quantum Sense video series. Thanks for all the useful feedback to my last question. My question concerns a very short chunk of about 20 seconds beginning at 4:25 of this link:
At around 4:34, he says "B-alpha has to be the same eigenvector as alpha...
Hi. I hope everyone is well. I'm just an old person struggling to make sense of something I've read and I would be very grateful for some assistance. This is one of my first posts and I'm not sure all the LaTeX encoding is working, sorry. Your help pages suggested I add as much detail as...
Show that if there exists a nonzero, translation-invariant bounded linear operator ##T : L^p(\mathbb{R}^d) \to L^q(\mathbb{R}^d)## where ##1 \le p, q < \infty##, then necessarily ##q \ge p##.
Hi,
If ##|a\rangle## is an eigenvector of the operator ##A##, I know that for any scalar ##c \neq 0## , ##c|a\rangle## is also an eigenvector of ##A##
Now, is the ket ##F(B)|a\rangle## an eigenvector of ##A##? Where ##B## is an operator and ##F(B)## a function of ##B##.
Is there way to show...
Could you tell me if I have understood following about operators in QM correctly?
Wavefunction takes all generalized coordinates of the system as arguments.
for example if we have a system of proton and electron (in 3-dimensional space) then the wavefunction of this system has 7 arguments...
Hello folks,
I need to show that a unitary operator obeys <Af,Ag>=<f,g>, where A is a unitary operator. However, I am technically not yet given the fact, that the adjoint of A is equal to its inverse, and that is the problem. I have no clue how to prove the given task without using the...
Knowing that to be Hermitian an operator ##\hat{Q} = \hat{Q}^{\dagger}##.
Thus, I'm trying to prove that ##<f|\hat{Q}|g> = <\hat{Q}f|g> ##.
However, I don't really know what to do with this expression.
##<f|\hat{Q}g> = \int_{-\infty}^{\infty} [f(x)^* \int_{-\infty}^{\infty} |x> <x| dx f(x)] dx##...
Suppose you take a Schroedinger-like equation $$-\psi''+F(x)\psi=0$$. (E.g. F(x)=V(x)-E, and not worried about factors of 2 etc.) This is positive definite if $$\int \left( \psi'^2+F(x)\psi^2 \right)dx>0$$. Is so, you can write this as the product $$(d/dx+g(x))(-d/dx+g(x))\psi=0$$, i.e. as...
Using the formula in 'relevant equations' I calculate
$$div(fA) = \nabla(fA) = (\nabla f) \cdot A + f \nabla \cdot A$$
$$3r^2 \cdot (x^2, y^2, z^2) + r^3 \cdot (2x + 2y + 2z)$$But the answer is
$$3r \cdot (x^3 + y^3 + z^3) + r^3 \cdot (2x + 2y + 2z)$$
I find no way of easily turning ##3r^2...
Hi Pfs
i have 2 matrix representations of SU(2) . each of them uses a up> and down basis (d> and u>
If i take their tensor product i will get 4*4 matrices with this basis:
d>d>,d>u>,u>d>,u>u>
these representation is the sum equal to the sum of the 0-representation , a singlet represertation with...
I've learned that in canonical quantization you take a Lagrangian, transform to a Hamiltonian and then "put the hat on" the fields (make them an operator). Then you can derive the equations of motion of the Hamiltonian.
What is the reason that you cannot already put hats in the QFT Lagrangian...
I have a question about operators in finite dimension Hilbert space.
I will describe the context before asking the question.
Assume we have two quantum states | \Psi_{1} \rangle and | \Psi_{2} \rangle .
Both of the quantum states are elements of the Hilbert space, thus | \Psi_{1} \rangle , |...
Quantum states are most often described by the wavefunction ,##\Psi##. Variable ,##\Psi(x_1x_2\dots x_n) \Psi^*(x_1x_2\dots x_n)## defines probability density function of the system.
Quantum states can also be described by the density matrices (operators). For a pure state, density matrix is...
##\langle T(f), g \rangle = \int_{0}^{1} \int_{0}^{x} f(t) dt ~ g(t) dt##
As ##\int_{0}^{x} f(t) dt## will be a function in ##x##, therefore a constant w.r.t. ##dt##, we have
##\langle T(f), g \rangle = \int_{0}^{x} f(t) dt ~ \int_{0}^{1} g(t) dt##
##\langle f, T(g)\rangle = \int_{0}^{1} f(t)...
I'm really not sure what the question expects me to do here but here is what I do know. If the state is an eigenstate it should satisfy the eigenvalue equation for example;
$$\hat{H} f_m^l = \lambda f_m^l$$
but is the question asking me to use each operator on each state? How do I know if...
I've tried figuring out commutation relations between ##L_+## and various other operators and ##L^2## could've been A, but ##L_z, L^2## commute. Can someone help me out in figuring how to actually proceed from here?
We've two operators ##\hat{a}##,##\hat{b}##. I know their position representation ##\langle r|\hat{b} \mid \psi\rangle=b##
##\langle r|\hat{a}| \psi\rangle=a
##
Is it generally true that the position representation of the combined operator ##\hat{a}\hat{b}## is ##a b## where ##a, b## are the...
Hi Pfs
I read this answer in
https://quantumcomputing.stackexchange.com/questions/136/if-all-quantum-gates-must-be-unitary-what-about-measurement
Quantum measurements are special cases of quantum channels (CPTP cards). Stinespring dilation states that any quantum channel is realized by...
I have to show that for two bounded operators on Hilbert spaces ##H,K##, i.e. ##T \in B(H)## and ##S \in B(K)## that the formula ##(T \bigoplus S) (\alpha, \gamma) = (T \alpha, S \gamma)##, defined by the linear map ##T \bigoplus S: H \bigoplus K \rightarrow H \bigoplus K ## is bounded...
I first Normalise the wavefunction:
$$ \Psi_N = A*\Psi, \textrm{ where } A = (\frac{1}{\sum {|a_n^{'}|^{2}}})^{1/2} $$
$$ \Psi_N = \frac{2}{7}\phi_1^Q+\frac{3}{7}\phi_2^Q+\frac{6}{7}\phi_3^Q $$
The Eigenstate Equation is:
$$\hat{Q}\phi_n=q_n\phi_n$$
The eigenvalues are the set of possible...
Hi,
I want to measure spin components of a ground state of some models. These ground states are obtained by ED. The states for constructing the Hamiltonian are integers representing spins in binary. As the ground state (and the other eigenvectors) are now not anymore in a suitable representation...
Hello! If I have a molecule in Hund case a, I can write its wavefunction (electronic + rotational) as ##|e,\Lambda,\Omega,S>|J,\Sigma,\Lambda,\Omega,M>##. I am not sure what happens if I apply, say, ##S_+## on this wavefunction (assuming I am not applying it to the top of the ladder), where this...
So we all know that the form of the momentum operator is: iħd/dx. And for energy it is iħd/dt. But how do we derive these operators?
The only derivations of the i have seen is where the schrødinger equation was used, but that makes the logic circular, because the Schrødinger-Equation is derived...
For ##N=1##, I have managed to prove this, but for ##N>1##, I am struggling with how to show this. Something that I managed to prove is that
$$\langle\psi |b_k^\dagger=-\langle 0 | \sum_{n=1}^N F_{kn}c_n \prod_{m=1\neq k, l}^N \left(1+b_m F_{ml}c_l \right)$$
which generalizes what I initially...
I would like to ask whether if operators ##A## and ##B## commute also operators ##e^A## and ##e^B## commute? Also I have a question is it possible that
##e^A## is matrix where all elements are ##\infty## so that ##e^A \cdot e^B-e^B\cdot e^A## has all elements that are ##\infty##?
Hello everyone! This is my first post here. I am trying out an argument that I've been sculpting, and I thought this might be a good community where I can get some good feedback.
My work is in data driven methods for dynamical systems, and in particular, I am an operator theorist. I have been...
I don't really know what I'm doing, I'd appreciate some nudges in the right direction. We defined ##\mathcal{S}## as the space of complex solutions to the Klein-Gordon equation, and for any ##\alpha, \beta \in \mathcal{S}## that ##(\alpha, \beta) =-\int_{\Sigma_0} d^3 x \sqrt{h} n_a j^a(\alpha...
For ##\hat{S}^+## and ##\hat{S}^{-}## operators for any given spin ##S## relation
\hat{S}^+|S,m \rangle=\sqrt{S(S+1)-m(m+1)}\hbar|S,m+1 \rangle
\hat{S}^-|S,m \rangle=\sqrt{S(S+1)-m(m-1)}\hbar|S,m-1 \rangle
Can someone please explain how we get those factors ##\sqrt{S(S+1)-m(m+1)}\hbar## and...
Have a look at O5 & O6 in Eqtns(5.4) . Why is there a (V+A) ?
(V+A) contains the projection operator which projects out the right Weyl from a Dirac spinor.
As per the Feynman rules of electroweak theory, there is a (V-A) assigned to each (Dirac) spinor-W boson vertex because W only couple to...
A recent thread by @coolcantalope was accidentally deleted by a Mentor (I won't say which one...), so to restore it we had to use the cached version from Yahoo.com. Below are the posts and replies from that thread.
The cached 2-page thread can be found by searching on the thread title, and is...
I want to show that ##[C, a_{r}] = 0##. This means that:
$$ Ca_{r} - a_{r}C = \sum_{i,j} g_{ij}a_{i}a_{j}a_{r} - a_{r}\sum_{i,j} g_{ij}a_{i}a_{j} = 0$$
I don't understand what manipulating I can do here. I have tried to rewrite ##g_{ij}## in terms of the structure...
Hi Pf,
I am reading this article about generalization of Pauli matrices
https://en.wikipedia.org/wiki/Generalizations_of_Pauli_matrices#Generalized_Gell-Mann_matrices_%28Hermitian%29
When i receive a qubit in a given density matrix , i can measure the mean values of the Pauli matrices by...
I'm trying verify the proof of the sum rule for the one-dimensional harmonic oscillator:
$$\sum_l^\infty (E_l-E_n)\ | \langle l \ |p| \ n \rangle |^2 = \frac {mh^2w^2}{2} $$
The exercise explicitly says to use laddle operators and to express $p$ with
$$b=\sqrt{\frac {mw}{2 \hbar}}-\frac...
According to this this the Darboux transformation preserves the discrete spectrum of the Haniltonian in quantum mechanics. Is there a proof for this? My best guess is that it has to do with the fact that $$Q^{\pm}$$ are ladder operators but I'm not sure.
The previous part was to show that ##a_+ \psi_n = i\sqrt{(n+1)\hbar \omega} \psi_{n+1}##, which I just did by looking at$$\int |a_+ \psi_n|^2 dx = \int \psi_n^* (a_{-} a_+ \psi_n) dx = E+\frac{1}{2}\hbar \omega = \hbar \omega(n+1)$$so the constant of proportionality between ##a_+ \psi_n## and...
The definition of the hermitian conjugate of an anti-linear operator B in physics QM notation is
\langle \phi | (B^{\dagger} | \psi \rangle ) = \langle \psi | (B | \phi \rangle )
where the operators act to the right, since for anti-linear operators ( \langle \psi |B) | \phi \rangle \neq...
I was seeing a lecture and the professor told that
i) you can measure an operator if it's hermitian, therefore observables are hermitian operators
ii) if you can measure two observables simultaneously, then those two observables(operators)
Is there any proof for this or is it some kind of rule...
How did you find PF?: Google
I know how to express Hamiltonian for scalar field written in field operators through the raising and lowering momentum operators, but I can't figure out how to do the same for the number of particles written in field operators: the 1/2E coefficient within the...
This is problem 18.3 from QFT for the gifted amateur. I must admit I'm struggling to interpret what this question is asking. Chapter 18 has applied Wick's theorem to calculate vacuum expectation values etc. But, there is nothing to suggest how it applies to a product of operators.
Does the...
So in particular, how could the determinant of some general "operator" like
$$ \begin{pmatrix}
f(x) & \frac{d}{dx} \\ \frac{d}{dx} & g(x)
\end{pmatrix} $$
with appropriate boundary conditions (especially fixed BC), be computed? And assuming that it diverges, would it be valid in a stationary...