I have a single technical question regarding a statement on page 7 of the paper "Dynamical quantum correlations of Ising models on an arbitrary lattice and their resilience to decoherence". The paper up until page 7 defines a general correlation function ##\mathcal{G}## of a basic quantum Ising...
I have question, how can I solve problem of particle in rigid box when one of the wall gets completely destroyed? At time t = 0 the right wall of box gets completely destroyed, left wall is still here( ψ(0) = 0 ), also at t = 0 we know that particle is in ground state.
How can I search for...
In a paper on quantum synchronization, they introduce the setup given in the attached 'Fig1.png'. I would like confirm a few concepts regarding this setup. The setup is described in the following way:
The general setup is shown schematically in Fig.1. Two
ensembles, each containing ##N##...
Suppose we have a quantum system ##Q## with an initial state ##\rho^{(Q)}##. The measurement process will involve two additional quantum systems: an apparatus system ##A## and an environment system ##E##. We suppose that the system ##Q## is initially prepared in the state ##\rho_{k}^{(Q)}## with...
Hi I am interested in finding a good measure of multipartite entanglement for pure quantum states represented in the Dicke state basis. Any recommendations of notes or texts in this regard would be appreciated. I am looking to start with the most basic measure of entanglement for states...
Before reading Bloch theorem i read something to get a feeling to what happens to the energy of electron in a periodic potential, in short what i read said:
Assuming we have a weak periodic potential from -π/a to π/a for example cos(2πx/a), we can write the electron wave function as: α|k>+β|k'>...
Suppose I have a 1-D harmonic oscilator with angular velocity ##\omega## and eigenstates ##|j>## and let the state at ##t=0## be given by ##|\Psi(0)>##. We write ##\Psi(t) = \hat{U}(t)\Psi(0)##. Write ##\hat{U}(t)## as sum over energy eigenstates.
I've previously shown that ##\hat{H} = \sum_j...
The Fundamental Theorem of Quantum Measurements (see page 25 of these PDF notes) is given as follows:
Every set of operators ##\{A_n \}_n## where ##n=1,...,N## that satisfies ##\sum_{n}A_{n}A^{\dagger}_{n} = I##, describes a possible measurement on a quantum system, where the measurement has...
I am interested in defining Krauss operators which allow you to define quantum measurements peaked at some basis state. To this end I am considering the Normal Distribution. Consider a finite set of basis states ##\{ |x \rangle\}_x## and a set of quantum measurement operators of the form $$A_C =...
Definition 1 The von Neumann entropy of a density matrix is given by $$S(\rho) := - Tr[\rho ln \rho] = H[\lambda (\rho)] $$ where ##H[\lambda (\rho)]## is the Shannon entropy of the set of probabilities ##\lambda (\rho)## (which are eigenvalues of the density operator ##\rho##).
Definition 2 If...
The following is a somewhat mathematical question, but I am interested in using the idea to define a set of quantum measurement operators defined as described in the answer to this post.
Question:
The Poisson Distribution ##Pr(M|\lambda)## is given by $$Pr(M|\lambda) =...
Consider the Gaussian position measurement operators $$\hat{A}_y = \int_{-\infty}^{\infty}ae^{\frac{-(x-y)^2}{2c^2}}|x \rangle \langle x|dx$$ where ##|x \rangle## are position eigenstates. I can show that this satisfies the required property of measurement operators...
How do you find the wave function Φα when given the Hamiltonian, and the equation:
aΦα(x) = αΦα(x)
Where I know the operator
a = 1/21/2((x/(ħ/mω)1/2) + i(p/(mħω)1/2))
And the Hamiltonian,
(p2/2m) + (mω2x2)/2
And α is a complex parameter.
I obviously don't want someone to do this question...
I was looking for questions to practice normalizing a wave function, so I visited the following online pdf, http://people.physics.tamu.edu/syeager/teaching/222/hw1solution.pdf. The first question was to find the normalization constant, A of ψ(x) = A cos (2πx/L) for (−L/4) ≤ x ≤ (L/4). After...
The adagium of most quantumphysics-afficionado's is: "Shut up and calculate" - 'learn the formalism'. So I started with Leonard Susskind's 'Theoretical minimum' textbooks.
So now I know a little (very little) about the formalism, I started to wonder to which extent I have to go to educate...
Homework Statement
Hello,
I'm just curious as to whether I'm going about solving the following problem correctly...
Problem Statement:
A particle mass m and charge q is in the ground state of a one -dimensional harmonic oscillator, the oscillator frequency is ω_o.
An electric field ε_o is...
The atomic orbital refers to the physical region where the electron can be calculated to be present, as defined by the particular mathematical form of the orbital (the statement is extracted from atomic orbitals-wiki).
The picture of 1s orbital seems to signify that electron can exist in the...