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.
I'm Canadian and looking into quite a few different graduate programs in Physics. I am still quite open to different opportunities, and have found some interesting Master's programs (both MSc and MASc) here that are funded. But outside of Canada, I was looking into applying for graduate programs...
Temperature of a system is defined as
$$\left( \frac{\partial \ln(\Omega)}{ \partial E} \right)_{N, X_i} = \frac{1}{kT}$$Where Ω is the number of all accessible states (ways) for the system. Ω can only take discrete values. What does this mean from a mathematical perspective? Many people say we...
Fermi's golden rule contains a term that is the density of the final states ##\rho(E_{final})##. For my problem we have no time depending potentials so that's the same as ##\rho(E_{initial})##.
If I understand the definition of ##\rho## correctly, it's the number of states in an interval...
I Have a question about how we arrive at the probabilities for the wavefunction collapsing to some specific value for an observable.
As far as I'm aware, the wavefunction is a superposition of possible states depending on the observable we try to measure.
Lets say I want to measure observable...
Homework Statement
Hey, the no-cloning theorem states, that arbitrary quantum states cannot be cloned by any circuit.
It is, however, possible to clone orthogonal states.
What would a circuit performing this action look like?
Homework Equations
Relevant equations: I am assuming you all now...
The quantum states ##\psi(x)## of the infinite square well of width ##a## are given by
##\psi(x) = \sqrt{\frac{2}{a}}\sin\Big(\frac{n \pi x}{a}\Big),\ n= 1,2,3, \dots##
Now, I understand ##n \neq 0##, as otherwise ##\psi(x)## is non-normalisable.
But, can't we get additional states for...
Guys
I have a doubt
When we calculate the trial function
We do it for the wave function of the orbitals
Right in order to get the total orbital energy
(Which included the energy of the electron) and that of the orbital
Well my question
Is does the orbital possess
Some energy even if the electron...
Hello
I am confused and I can't figure out what is meant by phase when it comes to quantum mechanics for single photons and coherent states as I am a new to this field.
Best regards
I am looking over my notes for quantum mechanics, particularly for electronic state classification for nitrogen.
At ground state, nitrogen atom's 1s and 2s shells are fully filled and the 2p shell is half filled, thus the configuration is:
##2s^2 2p^3##
There are 3 different angular momentum...
Homework Statement
Given a orthonormal basis of the hilbert space of qutrit states: H = span (|0>, |1>, |2>)
write in abstract notation and also a chosen consistent matrix representation, the states
a) An equiprobable quantum superposition of the three elements of the basis
b) An...
Homework Statement
Construct the decompositions ##\mathbf 2 \otimes \mathbf 2 = \mathbf 3 \oplus \mathbf 1##, where ##\mathbf N## is the representation of su(2) with ##\mathbf N## states and thus spin j=1/2 (N-1).
Homework Equations
Substates within a state labelled by j can take on values -j...
I have to find a unitary transformation that takes me from one quantum state to another (or if there is such a transformation), given the two quantum states in matrix form. The matrices are huge (smallest is 16x16) , so doing it on paper is not an option. Does anyone know how I can do this in...
Hi All
Thanks for welcoming me to the physics forum. I am reading Greiner and Mueller's Quantum Mechanics: Symmetries and am stuck at not understanding the vector meson ( rho meson)'s spin states.
For S=1 we get three states -1, 0, and 1.
Prof. Mueller separated them as a rho +/-1, and rho 0 ...
Homework Statement
I figured out 4a, but I'm just struggling a bit with 4b.
Homework Equations
Relevant websites highlighted above (respectively):
http://www.nist.gov/pml/data/handbook/index2.cfm
http://physics.nist.gov/PhysRefData/ASD/lines_form.html
The Attempt at a Solution
This is...
Why mesons mixed states are defined as SOMETHING +/- SOMETHING [+/- SOMETHING] normalized by 1/sqrt(2) or 1/sqrt(3), So the sum uses quotient +1 or -1.
But in electroweak symmetry breaking charged W boson is defined as W1 (+/-) i*W2, so the quotient is +i or -i. So why mesons never use...
Hello,
I am a physics major and my friend is on a research vessel in the Arctic and can only operate email from the limited internet access there. I do not know organic chemistry so I was hoping someone could tell me if this was right (it is for homework when she returns; not in relation to her...
35g of h2o(g) at 380K flows into 300g of h2o(l) at 300K. Cp(l)=4.18kJ/K*kg and ΔH(condensation)= -2257kJ/kg.
I need to calculate the final temperature when the system reaches equilibrium.
Is the heat capacity for the h2o gas different than h2o liquid? Can you calculate heat capacity using...
Homework Statement
a)Find the densities of states 0.08 eV above the conduction band edge and 0.08 eV below the valence band edge for germanium. Be careful with units and be sure to give the units for your answer.
b) Find the volume density of states (i.e. number of states per unit volume)...
I was watching some Steve Spicklemire QM videos and had a question/check my knowledge..
When we measure a the state of a system, say a particle in a box or a quantum harmonic oscillator (QSHO), we "collapse" the superposition of the system and end up with one eigenstate and one eigenvalue...
Homework Statement
Two particles, their spin are 1/2.
The hamiltonian is ##H=\gamma s_1 \cdot s_2##
At t=0, the state ##|\alpha(0)>## is such as ##s_{1z}|\alpha(0)>=\hbar/2 |\alpha(0)>## and ##s_{2z}|\alpha(0)>=\hbar/2 |\alpha(0)>##. Find the state ##|\alpha(0)>##.2. The attempt at a...
Hey all,
I'm reading through an anecdotal work about the philosophical foundations of quantum field theory and the authors keep referring to states having the ability to be "sharp." As in it's possible for P to be sharp if the system is mixed, where P is some property of the system. Thanks! IR
I'm doing some personal research on how matter interacts with radiation. Specifically, I am looking through the treatment of Bransden and Joachain. I've taken two semesters of quantum in the past (a while ago), but now I'm coming across something that I've either never seen or never stopped to...
All textbooks and material that I've read on the topic state that the deuteron being a weakly bound system, has no excited state. They also go on to state that the deuteron exists as a mixture of ##^3 S_1## and ##^3D_1## states.
So, are these states degenerate in energy? That is, are both of...
Doesn't quantum teleportation show us that there are in fact at most 4 possible quantum states for a single qbit?
I mean, you are guaranteed to reproduce the completely arbitrary and unknown teleported state by doing one of 4 possible operations with your side of the entangled pair. You can even...
Mesons: hadrons with integer spin, usually quark-antiquark states
I came across this statement in a pdf of a powerpoint. Unfortunately the presentation is so badly formatted (missing images, content overlapping content, etc.) that it's hard to follow and I can't see if he ever describes mesons...
Hi,
if we adopt the convention, a^{\dagger}_\textbf{p} |0\rangle = |\textbf{p}\rangle
then we get a normalization that is not Lorentz invariant, i.e. \langle \textbf{p} | \textbf{q} \rangle = (2\pi)^3 \delta^{(3)}(\textbf{p} - \textbf{q}) .
How do I explicitly show that this delta...
I'm a litte confused about spin triplet and singlet states. How do we know that for ↑↓+↓↑ the total spin S is 1, and for ↑↓-↓↑ the total spin S is 0?
Also, how is total ms computed for these two states? (I understand that they are both 0, but not sure where that comes from)
Thank you very much...
two questions:
1. besides using Ehrenfests theorem, is there another way of showing that the expectation value of momentum is zero in a stationary state ? (I don't see it when simply applying the definition on the stationary solution)
2. If we have a state that is a superposition of...
Hey!
How are the two m=0 spin states (<up,down> + <down,up>) and (<up,down> - <down,up>) physically different? I realize that according to the math, the first one has a total spin of ##2 \hbar## while the second has a total spin of ##0##. But wouldn't you, intuitively, expect both states to...
Hi everyone! I'm a freshman in the Physics BSc at the university of Rome, and I've been reading here and there threads talking about courses, minors, majors and else, and I was just wondering how does this work, because I can't get out of my confusion while trying to understand it lol.
In my...
I have some troubles in finding coefficients of superposition of states.
I have 2 particles, their spins are s1=3/2 and s2=1/2.
At t=0, the system is described by |a(0)>=|3/2, 1/2, 1/2, 1/2>
I have to find |a(t)>.
I have thought to proceed in the following way:
1) use the basis |s, s_z>...
Hello everybody.
I'm interested in some problems of bound states in external fields in QFT (especially QED).
I wonder are there any lectures/books or reviews which provide modern treatment of this subject?
I would like to learn more about general formalism and applications in QED (I allready...
Hoping this is in the right section! The module is nuclear and atomic physics but it crosses over into quantum occasionally.
I've attached an image of the bit I'm trying to work out.
I've got an exam on this topic in just over a week, so sorry if these posts get annoying, I have a feeling I'm...
In the U.S.A., states have been divided into red and blue. Who got to choose this? If I were a decider for a political party, I would want the "other guy" to be red. There have been notorious regimes that have had a red flag. A map with an increasing hord of red looks disturbing. Is there...
as you have learned about the states of matter in high school, there are three states of matter (just assume i know nth about plasma or any other things else first), and when change of states occur energy is supplied to the matter to increase its potential energy while keep kinetic energy...
I have been following a series of Leonard Susskind's lectures called 'Quantum Entanglements' (Part 1). In general, he explains how to find the probabilities of measurements of spin ½ particles' states, both single particles and pairs of them. I have learned the following: how to use the 2x2 spin...
The Purcell effect is when an atom placed inside a high finesse cavity with a very small mode volume gets an increase in the spontaneous emission rate. I've tried to find correct explanation for this effect, but it seems hard to find, except that it comes from an increase in the vacuum density...
I need to find the total number of states in a 1D monatomic lattice using the density of state equation g(ω), and I am having a hard time doing so. I'm fairly certain all I need to do ins integrate it, but this is proving to be a greater challenge than I thought it would...
Max Tegmark in his paper “Many worlds in context” http://arxiv.org/abs/0905.2182
Argues that …. .“Everett’s MWI is simply standard QM with the collapse postulate removed, so that the Schrödinger equation holds without exception”. He also argues that from this we can deduce that not only...
Homework Statement
A quantum-mechanical harmonic oscillator with frequency ω has Hamiltonian eigenstates |n with eigenvalues En = (n + 1/2) ħω. Initially, the oscillator is in the state (|0> + |1>)/√2. Write down how the state of the oscillator evolves as a function of time t. Calculate the...
Dear all,
In his book chapter " Green’s Function Methods for Phonon Transport Through Nano-Contacts", Mingo arrives at the Green's function for the end atom of a one dimensional lattice chain (each atom modeled as a mass connected to neighbouring atoms through springs). He gives the green...
It came to me just now that because we can always take the Fourier transform of a well-behaved function, this means we can think of any such state as a superposition of free-particle momentum eigenstates. E.g., the Hermite polynomial eigenfunctions of the harmonic oscillator. They have a...
If we have a system of two electrons, addition of angular momentum tells us that the spin states of the composite system can be decomposed into those of the two electrons as follows
|1,1>=|+>|+>
|1,0>=(|+>|-> + |->|+>)√2
|1,-1>=|->|->
|0,0>=(|+>|-> - |->|+>)√2
where the states are |s,ms> for the...
I am trying to calculate the density of energy states in a two dimensional box. The way my professor did this is by first calculating the amount of states with their energy less than some energy e and taking its derivative with respect to e. In order to see how many energy states there are with...