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.
Hello,
I'm stuck with this exercise, so I hope anyone can help me.
It is to prove, that the density of states of an unknown, quantum mechanical Hamiltonian ##\mathcal{H}##, which is defined by
$$\Omega(E)=\mathrm{Tr}\left[\delta(E1\!\!1-\boldsymbol{H})\right]$$
is also representable as...
Hi, guys.
If you are given one state of the baryon decuplet (the upper-right state ##\Deltaˆ{++}=uuu##, for instance), you can use the ladder operators to get the other states of the decuplet.
When I apply ##T_-## to uuu and normalizing, I get ##\frac{1}{\sqrt{3}}(duu+udu+uud)##. However, in...
Hi,
I know how to calculate density of states for both cases, but it is not clearly to me how I can go from 3D case to 2D. I have energy from infinite potential well for 3D
$$E=\frac{\hbar \pi^2}{2m}(\frac{n_x^2}{l_x}+\frac{n_y^2}{l_y}+\frac{n_z^2}{l_z})$$
let make one dimension very small...
Hello!
When computing the density of states of electrons in a lattice, a material with dimensions L_x, L_y, L_z can be considered. The allowed \mathbf{k} vectors will have components
k_x = \displaystyle \frac{\pi}{L_x}p
k_y = \displaystyle \frac{\pi}{L_y}q
k_z = \displaystyle \frac{\pi}{L_z}r...
Why cannot we represent mixed states with a ray in a Hilbert space like a Pure state.
I know Mixed states corresponds to statistical mixture of pure states, If we are able to represent Pure state as a ray in Hilbert space, why we can't represent mixed states as ray or superposition of rays in...
We are taught that the forces of attraction in a liquid are lesser than those in a solid. What is the reason? Is it because the intermolecular spaces are large or is it because the individual attractive force of the molecule is less?
If I have a spin 1/2 particle eg electron in an isolated box can I state for definite that there is a 50% chance of it being spin up and 50% spin down ?
If I know the probability of it being spin up and spin down how do I know if it exists as a pure state of a superposition of spin up and spin...
Homework Statement Consider the following example from a previous exam. We are to predict the spin and parity for F(A=17,Z=9), Florine, in the ground state and the first two excited states using the shell model.
Ground state:
Neutrons: (1s 1/2)^2 (1p 3/2)^4 (1p 1/2)^2
Protons: (1s 1/2)^2...
I have a question, and it is this: why is it that your hand can go through a gas or liquid while the same can't be done with solids? Is it because of density?
Homework Statement
What are S, L and J for the following states: ##^1S_0, ^2D_{5/2} ^5F_1, ^3F_4##
Homework Equations
The superscript is defined as: 2S + 1
The subscript is defined as: J = L + S
The letter denotes the angular momentum number (s, p, d, f...) starting at s = 0.
The Attempt at a...
Homework Statement
The three lowest energy states of an infinitely deep square well (of width L, between x=0 and x=L) are:
Ψ1(x,t) = N sin(πx/L) e-iω1t
Ψ2(x,t) = N sin(2πx/L) e-iω2t
Ψ3(x,t) = N sin(3πx/L) e-iω3t
N = sqrt(2/L) is the normalization, to make the total probability = 1.
Each wave...
'In the SU(3) quark model there are two singlet vector states $$|\omega_8 \rangle = \frac{1}{\sqrt{6}} \left(|u \bar u \rangle + |d \bar d \rangle - 2 |s \bar s \rangle \right) $$ belonging to the octet and the pure singlet state $$|\omega_1 \rangle = \frac{1}{\sqrt{3}} \left(|u \bar u \rangle +...
Hello, I am a 40 year old Computer Scientist by education and profession. Education in general is my hobby. I am currently listening to a lecture on quantum mechanics: The Teaching Company's Quantum Mechanics Physics of the Microscopic World. Very good. So please excuse my nievity and ignorance...
Homework Statement
Here is the problem: http://imgur.com/XEqE4SY
Homework Equations
|psi_s_ms> = |s, ms> ⊗ Σ D_i_j |psi_i, psi_j>[/B]The Attempt at a Solution
I know the singlet state in the |s, ms> basis is |0,0> = (1/sqrt(2))[ |up, down> - |down, up>] and that the hamiltonian for this...
Can someone explain the difference using concrete examples. I will attempt to explain my current understanding by example;
A H atom has different energy levels which can be exactly described by algebraic functions with quantum numbers n, l etc.
An electron can be excited from say the ground...
Looking (if possible for some of you) a concise but non mathematical explanation of the terms localization and delocalization?
This questions is related to Quantum Molecular Physics. When reading a paper of Spectroscopy and allowed transitions, I encounter the following phrase " [Intersystem...
Can a state only be formulated with respect to an observable in consideration? That is to say, does the formulation of the state depend on the particular observable in consideration?
Thanks.
I got (very) confused about the concept of states, pure states and mixed states.
Is it correct that a linear combination of pure states is another pure state?
Can pure (and mixed) states only be expressed in density matrices?
Is a pure state expressed in a single density matrix, whereas mixed...
I'm having trouble with the mathematics of tensor products as applied to Bell states.
Say I have the state
\begin{align*}
\left|\psi\right> &= \frac{1}{\sqrt{2}} \left(\left|0\right>_A \otimes \left|0\right>_B + \left|1\right>_A \otimes \left|1\right>_B\right)
\end{align*}
How would the...
Why is the triplet state space wave function ΨT1=[1σ*(r1)1σ(r2)-1σ(r1)1σ*(r2)] (ie. subtractive)? How does it relate to its antisymmetric nature?
Also, why is this opposite for the spin wave function α(1)β(2)+β(1)α(2) (ie. additive)? And why is this one symmetric even though it describes the...
Homework Statement
I'm going back through some homework as revision, and came across this problem. It was marked as correct, but now I'm thinking it's unconvincing...
For a particle in an infinite square well, with ##V = 0 , 0 \leq x \leq L##, prove that the stationary eigenstates are...
Hi all! Sorry if this question is stupid. The the time-independent schrodinger equation describes energy for a time-independent system, and the time-dependent schrodinger equation describes the time evolution of the wavefunction. So, how would you describe the energy for a time-dependent system...
The first spin analyser is orientated on the z-axis and the second is in a arbitrary N-direction.
My thought process I can't get past is below
If I find particle 1 to have spin up in Z-direction, the state collapses and the second must be spin down in the Z-direction for the particle at the...
The triplet spin state with a normalisation constant of 1/√2 and the singlet spin state with the same normalisation constant... Where on Earth is this normalisation constant derived from? I've been scouring the Griffiths intro to quantum mechanics textbook and can't find info on it.
Spin up and spin down states in the x direction can be written as
|Upx> = 1/ √2 ( |Upz> + |Downz> )
and
|Downx> = 1/ √2 ( - |Upz> + |Downz> )
My textbook just stated the above facts without referencing why and I've been going through the spin chapter for a while now and I can't see it. Why...
Hi all, I have a question about Slater Determinant for excited states.
Let's say we want to construct approximate (2 level) wavefunction of He in some certain state. Since we have two electrons in two level system with spin in consideration, we can construct total of 4 different wavefunctions...
Im having trouble with my thought process for spin states of a system of two electrons
Using Total Spin 'S' and Total spin mag quantum numbers 'MS' as state ket |S MS>
My textbook states...
" Three Symmetric Spin states
Triplet spin stats for twin identical spin -1/2 particles
| Up Up> = |S...
Homework Statement
I am trying to calculate the ratio of the density of states factor, ##\rho(p)##, for the two decays:
$$\pi^+\rightarrow e^++\nu_e~~$$ and $$\pi^+\rightarrow \mu^++\nu_{\mu}~~$$
Homework Equations
##\rho(p)~dp=\frac{V}{(2\pi\hbar)^3}p^2~dp~d\Omega##
Which is the number...
I am not sure exactly what E = mc^2 means.
1. Does it simply means if we were able to convert mass into energy this is the amount of energy.
2. That mass and energy are different states of the same thing. An example would be water which can either be a solid (ice), a liquid (water) or a...
Homework Statement
The problem is given above. I am struggling on the first two parts, where I am tasked with finding gamma and beta.
Homework Equations
For spin one half states in arbitrary directions, I know that psi = a*|n;+> + b*|n;-> .
|n;+> = cos(theta/2)|+> +sin(theta/2)*ei*phi|->...
I have googled it and cannot find anything. Apparently the rule that transition metals want full or half-full orbitals is false. I understand why the 4s orbital would be lost but I don't understand why some d electrons would be lost. For example in Mn6+, the electron configuration would be [Ar]...
Homework Statement
I apologize, this is not really a homework problem. I have an exam coming up, and I need to be able to explain the difference between a stationary/non-stationary quantum state in a qualitative way, and in what cases these states have time dependent probabilities. I am hoping...
I'm reading through some lecture notes for QM in a subsection about stationary states where the definition of orthonormality involving a kronecker delta \int_{-\infty}^{\infty}\psi_n(x) \ \psi_m^*(x)dx=\delta_{m,n}and the formula for some wavefunction that is a superposition of energy...
Hi, I am about to work on the problem of trying to find a renormalization program for bound states in QFT. Any suggestions/advice on where to start would be much appreciated.
If I try to send a vertically polarized photon through one slit and a horizontally polarized photon through the other slit, they actually go through both slits.
But when I measure and find out through which slit the horizontally polarized photon went, I automatically know that the vertically...
I think this is just a quickie. I'm interested in what is assumed about entangled photons/particles before they are observed. Is it correct to assume that the photons/particles exist in all possible states simultaneously?
Thank you.
It is easy to show that when you have a quantum system, let's think for example in electrons in a metal, then there appears summation over electron states of the form, e.g. for the energy for a free electron gas at T=0K:
##E=2 \sum_{k\leq k_f} \frac{\hbar^2}{2m}k^2##
Where ##k_f## denotes the...
Hello,
I am new to the forum, so I am directly stating my questions.
1)What determines the density of states of Phonons in a semiconductor?
2)Does degeneracy of semiconductors depend only on doping?
Thanks
If you raise the electron to other higher shell states, can light transmission throug
-h a SOLID BLACK opaque object.
Modified the original question because it was unclear.
I won't repeat the same question over, and over, but what I have said in previous questions may get repeated in the...
On Wikipedia, an article appear from which I quoted below. Here is something called Bose-Einstein correlation due to interference of wave character that I confuse with quantum entanglement.
I want to know if these BEC correlations are entangled or separable states...
Homework Statement
Hello all,
Im asked to construct the state | \frac{5}{2} , \frac{3}{2} \rangle from the eigenfunctions | L, L_z\rangle and the electron states | \uparrow \rangle and | \downarrow \rangle .
Homework Equations
Clebsch Gordon Coefficient's table
The Attempt at a...
The following is taken from page 13 of Peskin and Schroeder.
Any relativistic process cannot be assumed to be explained in terms of a single particle, since ##E=mc^{2}## allows for the creation of particle-antiparticle pairs. Even when there is not enough energy for pair creation, multiparticle...
I am wondering if my understanding of superposition concept is correct. Forgive me for not using QM braket notation, I am new on this site and don't know how to embed it in the post.
What confuses me about superposition concept is that people often say that some system can be in two (or more)...
Hi,
I recently saw a derivation that included:
[1] #CS = V_spatial * V_momentum
[2] #QS = #CS/h
(where # indicates it's the total number of the variable)
quantum states = QS; classical states = CS; h is Planck's constant
If possible, do you mind explaining or directing me to references...
Although strictly quantum mechanics is defined in ##L_2## (square integrable function space), non normalizable states exists in literature.
In this case, textbooks adopt an alternative normalization condition. for example, for ##\psi_p(x)=\frac{1}{2\pi\hbar}e^{ipx/\hbar}##
##...
Hi there people!
So my question is why you can see localized surface states within the band gap of the material with an STM. How is a tunneling circuit being established?
An example of a two-qubit state is one of the Bell states, for example:
lB> = 1/√2 (l00> + l11>)
In my book it is stated that the Bell states form an orthonormal basis for the set of two qubit states. But what exactly is the general form of a two-qubit state? Is it any vector of the form:
lq>...
From the Ehrenfest theorem, we know that the equation below is correct for any state ## \psi ##.
##m\frac{d^2}{dt^2}\langle x \rangle_{\psi} =-\langle \frac{\partial V(x)}{\partial x} \rangle_{\psi} ##
But then one of the definitions of coherent states is states for which the expected value of...