The United States of America is a federal republic consisting of 50 states, a federal district (Washington, D.C., the capital city of the United States), five major territories, and various minor islands. The 48 contiguous states and Washington, D.C., are in North America between Canada and Mexico, while Alaska is in the far northwestern part of North America and Hawaii is an archipelago in the mid-Pacific. Territories of the United States are scattered throughout the Pacific Ocean and the Caribbean Sea.
States possess a number of powers and rights under the United States Constitution, such as regulating intrastate commerce, running elections, creating local governments, and ratifying constitutional amendments. Each state has its own constitution, grounded in republican principles, and government, consisting of three branches: executive, legislative, and judicial. All states and their residents are represented in the federal Congress, a bicameral legislature consisting of the Senate and the House of Representatives. Each state is represented by two senators, while representatives are distributed among the states in proportion to the most recent constitutionally mandated decennial census. Additionally, each state is entitled to select a number of electors to vote in the Electoral College, the body that elects the president of the United States, equal to the total of representatives and senators in Congress from that state. Article IV, Section 3, Clause 1 of the Constitution grants to Congress the authority to admit new states into the Union. Since the establishment of the United States in 1776, the number of states has expanded from the original 13 to the current total of 50, and each new state is admitted on an equal footing with the existing states.As provided by Article I, Section 8 of the Constitution, Congress exercises "exclusive jurisdiction" over the federal district, which is not part of any state. Prior to passage of the 1973 District of Columbia Home Rule Act, which devolved certain Congressional powers to an elected mayor and council, the district did not have an elected local government. Even so, Congress retains the right to review and overturn laws created by the council and intervene in local affairs. As it is not a state, the district does not have representation in the Senate. However, since 1971, its residents have been represented in the House of Representatives by a non-voting delegate. Additionally, since 1961, following ratification of the 23rd Amendment, the district has been entitled to select three electors to vote in the Electoral College.
In addition to the 50 states and federal district, the United States has sovereignty over 14 territories. Five of them (American Samoa, Guam, the Northern Mariana Islands, Puerto Rico, and the U.S. Virgin Islands) have a permanent, nonmilitary population, while nine of them do not. With the exception of Navassa Island, Puerto Rico, and the U.S. Virgin Islands, which are located in the Caribbean, all territories are located in the Pacific Ocean. One territory, Palmyra Atoll, is considered to be incorporated, meaning the full body of the Constitution has been applied to it; the other territories are unincorporated, meaning the Constitution does not fully apply to them. Ten territories (the Minor Outlying Islands and American Samoa) are considered to be unorganized, meaning they have not had an Organic Act enacted by Congress; the four other territories are organized, meaning they have had an Organic Act that has been enacted by Congress. The five inhabited territories each have limited autonomy and a non-voting delegate in Congress, in addition to having territorial legislatures and governors, but residents cannot vote in federal elections.
Hi!
I'm struggling with the following question:
Show that if n quantum states ρ1, ..., ρn are pairwise perfectly distinguishable, they are also jointly perfectly distinguishable.
Perfect distinguishability means that there is a set of psd matrices \{E_{1}, ..., E_{n}\},\, \sum_{i} E_{i} =...
Let us consider QFT in Minkowski spacetime. Let ##\phi## be a Klein-Gordon field with mass ##m##. One way to construct the Hilbert space of this theory is to consider ##L^2(\Omega_m^+,d^3\mathbf{p}/p^0)## where ##\Omega_m^+## is the positive mass shell. This comes from the requirement that there...
Hi everyone! Sorry for the bad english!
I'm trying to understand the "delayed choice entanglement swapping" (avaliable in https://arxiv.org/abs/1203.4834 ) and (long story short) , in the article we have pairs of photons that are entangled in the ## \phi \pm ## Bell state and the photons...
In QM, states evolve in time by action of the Time Evolution Unitary Operator, U(t,t0). Without the action of this operator, states do not move forward in time. Yet even stationary states, like an eigenstate of energy, still contain a time variable – they oscillate in time at a fixed...
In my textbook, quantum states are infinite dimensional vectors. But I was watching a lecture on QM and the professor referred to ##|v> <u|## as itself being a quantum state. Also I saw online people saying the same thing.
Are tensor products just things that tell you whether or not the two...
I am trying to reproduce a very simple result that involved evaluating the refined index for a vector supermultiplet but ran into a snag. I hope someone will be able to clear that up easily.
Apparently for a half vector multiplet (meaning that we do not include the CPT conjugated states), the...
I'm having trouble picturing the energy states for some systems. For instance, I was reading Reif's Fundamentals of Statistical and Thermal Physics, and at some point he talks about the energy states of a pool acting as a heat reservoir interacting with a bottle of wine. The problem is that...
Hi, I'm currently working on showing the relation of quantum fidelity:
The quantum “fidelity” between two pure states ρ1 = |ψ1⟩⟨ψ1| and ρ2 = |ψ2⟩⟨ψ2| is given by |⟨ψ1|ψ2⟩|^2.
Show that this quantity may be written as Tr(ρ1ρ2).
I've been following the wikipedia page on fidelity but can't...
Protium atom has two low lying excited states with long lifetimes.
These are:
2s. Decay energy would be 121 nm, but forbidden (no angular momentum difference). Fastest allowed decay is two-photon emission, lifetime 0,15 s
Triplet 1s. Decay energy 211 mm. Prevalent decay single photon emission...
Most of the books I've seen they say that the first excited state of Helium (with two electrons, one in orbital 1s and other in 2s) can have the two electrons with parallel spin (orthohelium) or anti-parallel spin (parahelium).
If ##\operatorname{X_{↑}}{\left (n \right )}## represent the state...
I'm reading the following paper.
https://arxiv.org/abs/1409.1570
Is there an epistemic model of a qubit in which the number of ontic states is finite? I realize Spekkens toy bit discussed in the paper has only 4 ontic states, but it seems to only model a qubit that was prepared in one of 3...
EDIT: Questions have been revised below, those immediately following are for reference, jambaugh's kind reply was in direct response to these original questions.
Could a completely unitary (QM) process act on a set of particles in "completely identical quantum states" to cause them to time...
Hi
My question relates to existence of metastable states in atoms which help out laser production. Is there any physical reason why some orbits allow electrons to stay for comparatively longer time 10-3 s than others which allow only 10-8s?
Is this stay time same for all materials?
Please guide.
Hi,
I'm an undergrad, following my very first serious course in QM. We're following Griffith's book, and so far we're staying close to the text in terms of course structure.
Griffiths starts out his book by postulating that each and every state for any system \Psi must be a solution to the...
Suppose a set of basis vectors are eigenvectors of some operator. So they will provide a one dimensional representation of that operator in the vector space?
Could I have hundred times the ground state or there is a limit?
Is there a limit for excited magnetic momentum that if reached the nucleous explode or generate gammas?
I suppose If I excite it it would spin faster but proportional to quantum values. Note: there is a "theory" to avoid electron...
A question came up about deducing the number of possible energy states within a certain momentum ##p## using momentum space.
To make my question easier to understand, I deliberately chose ##p## and not a particular increment ##dp## and I assume a 2 dimensional momentum space with coordinates...
I've been reading a bit about the quantum confinement effect on nanowires, particularly how it changes the band structure. I'm trying to find an explanation on why the density of states splits into sub-bands. At the moment all I'm running into is 'because of the quantum confinement effect' which...
In Wikipedia's outline of the Many Worlds Interpretation of quantum physics https://en.wikipedia.org/wiki/Many-worlds_interpretation, it states "In many-worlds, the subjective appearance of wavefunction collapse is explained by the mechanism of quantum decoherence,...", yet I thought decoherence...
I'd like to see whether or not I understood correctly how massive particle states will transform under a homogeneous Lorentz transformation, in terms of the standard four-momentum ##k = (0,0,0,M)##. I suppose we can write $$U(\Lambda) \Psi \propto D^{(j)} (W(\Lambda)) \Psi$$ where ##U(\Lambda)##...
Holographic Relations for OPE Blocks in Excited States
https://arxiv.org/pdf/1809.09107.pdf
Jesse C. Cresswell†1 , Ian T. Jardine†2 , and Amanda W. Peet†§3 †Department of Physics, University of Toronto, Toronto, ON M5S 1A7, Canada §Department of Mathematics, University of Toronto, Toronto, ON...
The MB energy distribution is: MB_PDF(E, T) = 2*sqrt(E/pi) * 1/(kB*T)^(3/2) * e^(-E/(kB*T))
How do I arrive at the density of states which hides inside the expression 2*sqrt(E/pi) * 1/(kB*T)^(3/2) ? I've only seen DOS that have "h" in them.. I want it to contain only E, pi, kB and T.. This is...
Homework Statement
Show that the coherent state ##|c\rangle=exp(\int \frac{d^3p}{(2\pi)^3}c(\vec{p})a^{\dagger}_{\vec{p}})|0\rangle## is an eigenstate of the anhiquilation operator ##a_{\vec{p}}##. Express it in terms of the states of type ##|\vec{p}_1...\vec{p}_N\rangle##
Homework Equations...
Homework Statement
Is the following matrix a state operator ? and if it is a state operator is it a pure state ? and if it is so then find the state vectors for the pure state.
If you don't see image here is the matrix which is 2X2 in MATLAB code:
[9/25 12/25; 12/25 16/25]
Homework...
Hello! In the calculation of the QED matrix element, it says in the book I read that we have to sum over the polarization states of the photon: $$\sum_\lambda \epsilon_\mu^\lambda\epsilon_\nu^{\lambda *}=-g_{\mu\nu}$$ I am a bit confused why do we do a summation over the orthonormal basis...
Moderator's note: This is a sub-thread spun off from https://www.physicsforums.com/threads/is-the-ground-state-energy-of-a-quantum-field-actually-zero.953766/.
I should have said that in certain cases in QFT, we can neglect “surface terms”. For example, the (on-shell) difference between the...
Hello,
I have read in several textbooks and articles of semiconductor physics that the valence bands are p-like state. So, even in the mathematical calculation in k.p theory, it is widely used, especially to define heavy holes and light holes states.
My question is: How acurate is this? Why do...
Hi,
I'm dealing with the following problem. I hope someone could help me with it.
Problem is about 2 interacting particles (spin: 1/2 each), with Hamiltonian Ho=-A( S_1z + S_2z) and perturbation H1={(S_1x)*(S_2x) - (S_1y)*(S_2y)}. The question asks to calculate the energies of all 4 states up...
Hello. I've been struggling for a day with the following problem on Quantum coherent states, so I was wondering if you could tell me if I'm going in the right direction (I've read the books of Sakurai and Weinberg but can't seem to find an answer)
1. Homework Statement
*Suppose a Schrödinger...
Hi, I just started a book on QFT and one of the first things that was done was switch from labeling states with their individual particles and instead label states by the number of particles in each momentum eigenstate.
In addition, some "algebras" (not sure if they qualify by the mathematical...
The BE-distribution for the case of only one state per energy level (gi = 1) is
ni = 1 / (exp(ui - μ)β - 1)
This is a reasonable and well defined distribution as far as I can see.
On the other hand the number of possibilities to realize a given distribution of bosons among k energy levels with...
I'm watching a lecture and the professor is talking about generic quantum states as
|\psi>
He's making the point that this state is very generic. It can represent anything. He references some examples like the polarization of a photon and the path of a photon and the spin of an electron...
We have a 1 dimensional infinite well (from x=0 to x=L) and the time dependent solution to the wavefunction is the product of the energy eigenstate multiplied by the complex exponential:
\Psi_n(x, t) = \sqrt{\frac{2}{L}} \sin(\frac{n\pi x}{L}) e^{-\frac{iE_n}{\hbar}}
Now, I want to create a...
I am trying to understand how to think about a state of the form:
|\psi \rangle=\alpha|H_A H_B\rangle+\beta|V_A V_B\rangle where |\alpha|\neq |\beta|
It is between pure entangled state and a classical state like \psi \rangle=|H_A H_B\rangle, but it is not mixture of the two either. So it seems...
Let's suppose I have a finite potential well: $$
V(x)=
\begin{cases}
\infty,\quad x<0\\
0,\quad 0<x<a\\
V_o,\quad x>a.
\end{cases}
$$
I solved the time-independent Schrodinger equation for each region and after applying the continuity conditions of ##\Psi## and its derivative I ended up with...
I'm watching a lecture on the intro to quantum computing.
See the attached image which will be useful as I describe my question.
So the professor says that we have this single photon and it's in this state, ## | 0 > ##.
He states that when we send this photon through a beam splitter that it...
I have a question (more like a curiosity) related to three-dimensional topological insulators, which support Dirac-like states at their surfaces. From the theory, it is well known that these states are immune to scattering from non-magnetic impurities, i.e. impurities that do not break...
I read this wiki and some of the references
https://en.wikipedia.org/wiki/Bound_state
But I can't really understand. For example the electron in hydrogen has specific energies and not general relations that the articles seem to claim.
Thanks
I am studying Quantum Cryptography and I am quite new in Quantum area. I have read an article and I found this confusing statement:
My questions:
1. The three stage protocol implementing multiphoton. What is the meaning of coherent states of mean photon number?
2. How to describe the quantum...
Am I understanding it correctly that if you keep acting with an internal 2-dimensional creation operator on a string you will get heavier and heavier particle from the 11-dimensional (26 dimensional) point of view? If so, how come we haven't observed those particles in the real life? Is it...
I'm to get the density of states of 1-dim linear phonons, with N atoms. I think it's a lot similar to that of 1-dim electrons, except that two electrons are allowed to be in one state by Pauli exclusion principle. To elaborate,
##dN=\frac{dk}{\frac{2π}{a}}=\frac{a}{2π}dk## for...
Can anyone with basic knowledge of Dicke States assist with explaining how we arrive at equation (4) in the paper 'Entanglement detection in the vicinity of arbitrary Dicke states': <Moderator's note: link fixed>
$$\langle J^2_{x} \rangle_{\mu} = \sum_{i_1,i_2} \langle J_{xi_{_1}} \rangle_{\mu}...
Hello!
The time reversal operator, ##\hat{\Theta}## transforms a Bloch state as follows:
##\hat{\Theta} \psi_{nk}=\psi^*_{nk}##.
How does one proceed to prove the condition that ##\psi_{nk}## and ##\psi^*_{nk}## must satisfy in order for our system to be time reversal invariant?
Thanks in advance!
Hello!
I want to know how does a parity transformation affect Bloch states! I always knew that parity takes the position vector to minus itself (in odd number of dimensions), but I have read that it also takes the Bloch wave vector to minus itself but I have not found a satisfactory proof of...
Homework Statement
Using the heats of fusion and vaporization for water, calculate the change in enthalpy for the sublimation of water:
H2O(s) --> H2O(g
Using the delta H value given in Exercise 24 and the number of hydrogen bonds formed to each water molecule, estimate what portion of the...
This thread refers to a paper I am working on.
The paper said in the model section that:
In the complete set of scattering states we distinguish two orthogonal set of eigenfunctions:
(i) the states
− →
ϕ incoming from the left, and (ii) the states
←−
ϕ incoming from the right. Away from...
In the algebraic approach, a quantum system has associated to it one ##\ast##-algebra ##\mathscr{A}## generated by its observables and a state is a positive and normalized linear functional ##\omega : \mathscr{A}\to \mathbb{C}##.
Given the state ##\omega## we can consider the GNS construction...