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.
Homework Statement
Find the wavelength of the radiation emitted when a hydrogen atom makes a transition from the n = 6 to the n = 3 state. Give answer in µm.
Homework Equations
z^2 / n^2 x 13.6ev
delta E = E2 - E1 = hv
The Attempt at a...
Homework Statement
I have to show that the Fock states are eigenstates for the operators {{\hat{a}}^{\dagger }} and/or {\hat{a}}
And I'm not totally sure how to show this.
Homework Equations
?
The Attempt at a Solution
I know that if I use the operators on a random Fock...
Hi,
Here's my problem, probably not that difficult in reality but I don't get how to approach it, and I've got an exam coming up soon...
An atom with total angular momentum l=1 is prepared in an eigenstate of Lx, with an eigenvalue of \hbar. (Lx is the angular momentum operator for the...
Homework Statement
I am trying to understand how we go about calculating the density of states in situations where the available quantum states are continuous, e.g. electrons in a white dwarf.
I am happy to accept the uncertainty relation (we learned to derive it as the product of the...
Hi, when we consider an N-particle (assume non-interacting) system, say putting them in a box; why do we always say the states of the system (e.g. when counting them to find the "density of states as function of energy") are just the products of single particle stationary states (i.e. energy...
Homework Statement
If the energy separation of two states is known for some atom, how can the same energy separation be calculated for the same two states for an ionized atom? i.e. if we know that the difference between the 1s^2 and the 1s2s states in Helium is something like 25eV, how could...
Hi all,
I'm doing some test prep for a Nuclear Physics course and working on a past paper. I've attached a photo of the question. The diagram is 3.19 in Krane. The course is based on Krane, and so the relevant chapter is Chp 5: Nuclear Models.
Problem description
The problem is to explain...
Homework Statement
The components of the initial state |\psi_i> of a quantum system are given in a complete and orthonormal basis of three states |\phi_1>, |\phi_2>, |\phi_3> by
<\phi_1|\psi_i>=\frac{i}{\sqrt{3}}
<\phi_2|\psi_i>=\sqrt{\frac{2}{3}}
<\phi_3|\psi_i>=0
Calculate the probability...
i have two questions that i am struggling with and i have tried all i can think of with them and i am still not getting the answers correct.
1)Estimate, using the Uncertainty Principle, the kinetic energy of an electron if it were bound in the nucleus.
Answer: ∼ 200 MeV for R ∼ 1 fm...
Can someone help me prove that tr(\rho^2) \leq 1 ?
Using that \rho = \sum_i p_i | \psi_i \rangle \langle \psi_i |
\rho^2 = \sum_i p_i^2 | \psi_i \rangle \langle \psi_i |
tr(\rho^2) = \sum_{i, j} p_i^2 \langle j | \psi_i \rangle \langle \psi_i | j \rangle
Where do I go from here? Thanks guys.
I'm reading the paper by D.B. Chklovskii where he quantitatively describes the appearance of strips of incompressible electron fluid in a 2DEG when a magnetic field is applied to it. What I don't get is the relationship between these strips of incompressibility and the edge states in the 2DEG...
Hey Guys,
Am working through Relativistic Quantum Mechanics: Wave equations by W.Greiner and have a simple question about the Klein-Gordon equation: is it fair to say that bound states only occur between -m<=E<=m? (c=1). There are a few problems where they show that you can get pair...
If I have SO42-, I can figure out that the oxidation state of each O ion is 2- and the sulfur ion must then be 6+. What does this number mean? What does it tell you about the electrons in that molecule?
Homework Statement
Explain why 2-bromopropane reacts with NaI in acetone over 10^4 times faster than bromocyclopropane. (Hint: examine the transition state for each of the reactions)
Homework Equations
The Attempt at a Solution
I understand this is a sn2 type reaction and...
Homework Statement
Give the number of states (energy of the state smaller than E<0) \Phi(E) of a spinless particle with mass m in the central potential V(\vec{r})=-\frac{a}{\left|\vec{r}\right|}.
Homework Equations
The Attempt at a Solution
Hi,
the hamiltonian of this problem...
When in history did we go from the States being sovereign and over the Federal government to the Federal government being sovereign and over the States?
The founders like Jefferson, Adams, Hamilton, Marshall and Webster all understood the States as sovereign with the right to secede.
It'd be great if you could help me clarify a few things in my head.
Firstly I've got written in my notes "quantum mechanics forbids spontaneous transitions from one energy level to another because energy eigenfunctions are time independent".
However this seems a bit of a circular...
Homework Statement
Rotation of a deformed nucleus is predicted to produce nuclear excited states with energies given by E(J)=J(J+1)hbar/2I. The first two excited states of 238 U are Jpi = 2+(0.045MeV) and Kpi=4+(0.148MeV). Show these energies are consistent with rotational excitation stating...
Hi guys
In some articles I've read, they all mention that the (local) density of states is related to the retarded Greens function for a non-interacting system by
-(1/π)Im[G(r,ω)] = LDOS(r,ω),
i.e. the imaginary part of the Greens function. The above relation holds because in k-space the...
Consider a particle in an infinite square well described initially by a wave that is superposition of the ground state and the first excited states of the well: Ψ(x,t = 0) = C[ψ1(x) +ψ 2 (x)]
(a) show that the value C =1/ 2 normalizes this wave, assuming 1 ψ and 2 ψ are themselves normalized...
Dear all,
In Density Functional Theory (DFT) the Kohn-Sham eigenvalues are used to construct the band structure and the density of states (DOS). For a 3D extended system the eigenvalues are determined up to a constant since there is no absolute energy reference, while for a 2D extended...
Hi I know that stationary states in a system with an even potential energy function have to be either even or odd.
Why does the ground state have to be even, and not odd? This is asserted in Griffiths, page 298.
Hi,
I stumbled upon this dilemma in a homework problem which involved 2D photon gas (unphysical, I know). How many polarization states are there for EM-radiation confined to 2D? In 3D it's 2, but how does it work in 2D? An EM-wave propagating in the z-direction can have its E-component...
Homework Statement
Part A)
Establish which of the following combinations of particles can exist in a state of I=1 :
a) \pi^0\pi^0
b) \pi^+\pi^-
c) \pi^+\pi^+
d) \Sigma^0\pi^0
e) \Lambda^0\pi^0
Part B) of the problem is:
In what states of isospin may exist the following systems?
f)...
Homework Statement
a) Enumerate the possible L and S for the 2s2p3p configuration.
b) Find the possible L and S for the 2p^23p configuration.
Homework Equations
^{2S+1}L_J
S=0 (Singlet)
S=1 (Triplet)
The Attempt at a Solution
First of all, doesn't "enumerate" and "find the possible...
Hello,
this is quite a basic question I know, but something I'm not sure I've fully got my head around. In classical particle mechanics the dynamical variable is the position vector x, and in classical field theory the dynamical variable becomes the field \phi(x) , with x being relagated to...
How does one solve bound state problems in QFT(like an electron positron atom)? How does one identify the space of states. The Fock space seems to lose it definition when a bound state problem is discussed. There is also no meaning to wave functions or potentials that are used in standard...
Hi guys
I have an analytical expression f(x) for my density of states, and I have plottet this. Now, I also have a complete list of my Hamiltonians eigenvalues.
When I make a histogram of these eigenvalues, I thought that I should get an exact (non-continuous) copy of my plot of f(x). They...
What do mesocopic or even macoscopic superposition states mean? Can we look at a superposition, at a state |alive> + |dead> or |particle here> + |particle over here> ?
thank you
I've been following the lectures given by Leonard Susskind on Quantum Entanglement. In Lecture 6, he describes a simplified version of the two-slit experiment so that we can use finite dimensional spaces to describe the system (which is all we've learned so far).
He also uses what he calls...
Say you have a Yukawa potential (a.k.a. screened coulomb potential) V(r) = -\frac{e^2}{r}e^{-rq} where q is the inverse screening length, how would you find the critical q for having bound states? I'm working on reproducing N.F. Mott's argument about the critical spacing of a lattice of...
Hi everyone,
A QM question that I am stuck on:
Consider the addition of the spin of 2 electrons, s1=s2=½. Show
that there are one ms=1; two ms=0 and one ms=-1 states. Show the
4 spin states are given by:
a1a2
b1b2
(1/(sqrt(2)))(a1b2+b1a2)
(1/(sqrt(2)))(a1b2-b1a2)
I've used a...
In a system with two spin 1/2 particles ,
We now ask what are the allowed total spin states generated by adding the spins ${\bf S}= {\bf S}_1 + {\bf S}_2$ ,in fact, they are Singlet and Triplet Spin States
\left( \begin{array}{ll} |1,1\rangle & =\uparrow\uparrow\\ |1,0\rangle &...
Homework Statement
Consider an isolated system consisting of a large number N of very weakly interacting localized particles of spin 1/2. Each particle has a magnetic moment \mu which can point either parallel or antiparallel to an applied field H. The energy E of the system is then E =...
i have an equation for the density of states that depends on 1/(sqrt E). i have lots of coefficients to this
[Vm^{3/2} w_c ] / [2 sqrt {2} pi^2 hbar^2]
do these coefficients represent the degeneracy of the desity of states?
Homework Statement
A nucleus can exhibit vibrational and rotational collective motion. Write down the expression for the energy levels for each type of motion, taking care to explain the symbols used.
Discuss with the aid of calculations how you would decide which collective motion is...
i'm given either |0> or cos\phi|0> + sin\phi|1> by a fair coin toss.
and I don't know which state I'm given.
i need guess which state was chosen.
i think the method is to do a unitary operation on the states, and do the measurement,
but I'm not sure how to construct a unitary, and I'm still...
Hi. I'm studying the transition rates between a state a and a state b in the continuos level.
In the book "Physics of atoms and molecules" by Bransden and Joachain it is said:
We have to calculate the density of final states. To do this let the volume V be a cube of side L. We can impose...
I have a question regarding the possible oxidation states of metals. I understand how to find the oxidation state of a metal in a compound, that's pretty straightforward. What I'm interested in is finding possible oxidation states given only the name of the metal. For example, Cu has possible...
In terms of stationary states we have bound states and free(plane wave or Coulomb) states
Autoionizing states are free(E>0), e.g. continuum, but localized states(resonances). Hence
wavepackets consisting of a band of plane or Coulomb waves. I understand they may be long-lived, longer than the...
i was looking at the number line and its various axis and thought, this is a system for storing states of energy. whereupon when we input figures we actually send a quantified amount of energy into the network and the energy is bounce around according to the resistance it meets within the system...
Homework Statement
The ground state of _{6}Cl^{13} has spin-parity 1/2- and the next three excited states have values of 1/2+, 3/2- and 5/2+. Explain these values in terms of the shell model.The Attempt at a Solution
The problem is that i don't know what is being asked of me...i initially...
The multiverse theory states that there are an infanite amount of other realities, and that anything that can happen will hapen. How does this really work?
Anyone know the difference between how electron fill the orbitals as opposed to nucleons. And what are the special properties of systems with closed shell characteristics.
Hi,
I am trying to find an expression for the density of states of free two-dimensional electrons, as a function of energy, and I am really struggling.
I get that what I am looking for is the number of states per unit area of k-space per unit energy, and in general (3D), this is expressed as...
Let's say you have some quantum particle whose eigenvalues for some observable Q are either degenerate or non-degenerate. If you measure the observable and find it to be in a non-degenerate state, then you know that the wave function has collapsed onto this state. Now if you measure the...
I understand that all real-world applications can never attain 100% efficiency, whether it be referring to something mechanical, electrical, or some thermodynamic cycle.
While studying the Carnot cycle and learning about the upper limit of efficiency for thermodynamic cycles, I drew a blank...
Hi, I have a question about statistical mechanics.
How do you calculate the density of states for phonons and electrons in a d-dimensional system (at fixed chemical potential) and when the dispersion relation for the electrons is E(p)=A |p|^g and for the phonons is w=v|p|
To get the...
Is it perpetual? I think it will continue to be very large because the US is top dog. How many nations are likely to ask the US for their money back, and what could they possibly do to warrant the US to pay up?
People seem to like our money, so why not share?