What is States: Definition and 1000 Discussions

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.

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  1. Einj

    Variational Method and Bound States

    Homework Statement Consider a potential function V(x) such that: $$ \begin{cases} V(x)\leq 0\text{ for }x\in[-x_0,x_0] \\ V(x)=0 \text{ for }x\not\in[-x_0,x_0] \end{cases} $$ Show, using the variational method that: (a) In the 1-dimensional case \lambda^2V(x) always possesses at...
  2. Q

    Determine the energies of the three lowest energy states.

    Homework Statement A particle is confined to a two-dimensional box defined by the following boundary conditions: U(x, y) = 0 for \frac{-L}{2} ≤ x ≤ \frac{L}{2} and \frac{-3L}{2} ≤ y ≤ \frac{3L}{2}, and U(x, y) = ∞ outside these ranges. Determine the energies of the three lowest energy states...
  3. D

    Hydrogen atom eigenstate: proving orthogonality of states

    Homework Statement Hey dudes So here's the question: Consider the first excited Hydrogen atom eigenstate eigenstate \psi_{2,1,1}=R_{2,1}(r)Y_{11}(\theta, \phi) with Y_{11}≈e^{i\phi}sin(\theta). You may assume that Y_{11} is correctly normalized. (a)Show that \psi_{2,1,1} is orthogonal...
  4. R

    Density of states in D dimensions

    Homework Statement Find the density of states g(ε) for an ideal quantum gas of spinless particles in dimension d with dispersion relation  ε= α|p|s , where ε is the energy and p is the momentum of a particle. The gas is confined to a large box of side L (so V = Ld) with periodic boundary...
  5. L

    Singlet and triplet states of H2

    Homework Statement The wave function for a system of two hydrogen atoms can be described approximately in terms of hydrogen wave functions. (a) Give the complete wave functions for the lowest states of the system for singlet and triplet spin configurations. Sketch the spatial part of each...
  6. A

    Density of States: Definition & Explanation

    what do you mean by density of states ? can you please explain to it ?
  7. B

    Name of a switch that alternates between two states.

    I'm wondering what the name of a switch that alternates between two states only when depressed. An example would be a flashlight, where if you click it once, it turns on, and if you click it off, it turns off (no need to hold down the button to get a continuous light).
  8. A

    Why are photons released when electron jump states?

    I've always taken this for granted. Now I am looking for an answer. When electron jumps from a higher orbit to lower orbit it releases energy. Why is the energy in the form of photon? I will take another example which will make my question easy to understand. When two electrons are kept...
  9. A

    Number of States in a 1D Simple Harmonic Oscillator

    Homework Statement A system is made of N 1D simple harmonic oscillators. Show that the number of states with total energy E is given by \Omega(E) = \frac{(M+N-1)!}{(M!)(N-1)!} Homework Equations Each particle has energy ε = \overline{h}\omega(n + \frac{1}{2}), n = 0, 1 Total energy is...
  10. naima

    How do I express p1 |v1> + p2 |v2> for a mixture, not a pure state?

    Is there a way to write p1 |v1> + p2 |v2> if it is not a pure state but a mixture? thanks.
  11. D

    Set of Commuting Observables for pures states 2p-1,2px and 2s

    Hi, Here I have a question, apparently easy, but that I think it is a bit tricky. Homework Statement Indicate how can a hydrogen atom be prepared in the pure states corresponding to the state vectors ψ2p-1 and ψ2px and ψ2s. It is assumed that spin-related observables are not...
  12. C

    Differences between the triplet and singlet states

    What are the differences between the triplet and singlet states. triplet state-- parallel spins-- S=1 , 2S+1=3 Singlet state-- Paired spins---S=0 , 2S=1= 1 singlet state has paired spins of electrons in the same orbit, thus there are repulsion force between the two electron in the same...
  13. M

    Can exited states exist without a ground state?

    Hello everybody, I have a question which might be silly. Nevertheless: Can exited states exist if you know that the ground state do not exist? Will in such a case first exited state become the ground state? Thanks.
  14. C

    Schrodinger half spin states expectation values

    Homework Statement What is the expectation value of \hat{S}_{x} with respect to the state \chi = \begin{pmatrix} 1\\ 0 \end{pmatrix}? \hat{S}_{x} = \frac{\bar{h}}{2}\begin{pmatrix} 0&1\\ 1&0 \end{pmatrix}Homework Equations <\hat{S}_{x}> = ∫^{\infty}_{-\infty}(\chi^{T})^{*}\hat{S}_{x}\chi...
  15. G

    Transition between excited states

    Homework Statement An atom in an excited state has a lifetime of 1.2 x 10 -8 sec; in a second excited state the lifetime is 2.3 x 10 -8 sec. What is the uncertainty in energy for the photon emitted when an electron makes a transition between these two levels? Homework Equations...
  16. I

    Not Sure if this belongs here but - Help with Matter States

    Forgive me as I have no formal secondary education so my actual knowledge of terms and what not is limited but I am working on a theory that has me wanting to explore the varying chemical states of matter and what defines them. For example, how Nitrogen can be both a gas and a liquid in room...
  17. H

    Coherent States: Ʃ(|α|2)n = 1?

    Hi guys, Just a quick question, is the following statement true (it seems to be implied in the article I'm looking at); Ʃ(|α|2)n = 1 (The sum over n=0 to infinity) Thanks to anyone who takes a look.
  18. K

    Do protons have excited states?

    Do protons and neutrons have excited states? This page shows some simulated shapes of protons. http://discovermagazine.com/2003/aug/breakprotons Do the different shapes have to do with different energy states of the proton?
  19. M

    Are Bound States Always Entangled in Quantum Mechanics?

    Hi folks -- quick question. I appreciate that entangled states in quantum mechanics may not be bound states. But when we have bound states, are the particles always entangled with one another? Thanks a lot!
  20. A

    Density of states free electron gas

    For a free electron gas the procedure for determining the density of states is as follows. Apply periodic boundary conditions to the free electron waves over a cube of side L. This gives us that there is one state per volume 2\pi/L3=2\pi/V And from there we can find the number of states at a...
  21. A

    Double delta function potential: two bound states vs one ?

    In the double delta function potential well, where one delta function ( -αδ(x) ) is at -a and one at +a, if the energy is less than zero, there can be either one or two bound states, depending on the magnitude of α...if α is large enough, there can be two bound states, but if α is small, there...
  22. ShayanJ

    Fermions and Coherent States: What's the Connection?

    I know coherent states are minimal uncertainty states and can provide a link from quantum to classical physics.But when I hear fermions can't have coherent states,or at least are limited in this sense,I can't see any relationship! What's the point? And...another thing...is there sth called...
  23. L

    Gaussian Integrals for Quantum States of well Defined Momentum

    Consider the Gaussian Integral (eqn 2.64).. is anyone able to explain how the constant of normalization is rationalised?
  24. H

    Why Do 4s Orbitals Fill Before 3d as Atomic Number Increases?

    Homework Statement Explain why, as the atomic number increases, the 4s electronic states fill before the 3d states. The fact that they fill first means they are lower energy. You must explain why they are lower energy. Homework Equations The Attempt at a Solution First, I'm aware...
  25. C

    Exploring Two Photon Bound States: Insights from Recent Research | Physics World

    With great interest I read an article about a paper where scientists were able to create two photon bound states ("molecules of light"). http://physicsworld.com/cws/article/news/2013/sep/26/physicists-create-molecules-of-light I was quite astonished since light normally does not...
  26. G

    Infinite well linear combo of states

    Homework Statement A particle of mass m is trapped in a one-dimensional infinite square well running from x= -L/2 to L/2. The particle is in a linear combination of its ground state and first excited state such that its expectation value of momentum takes on its largest possible value at...
  27. N

    Determining Energies of States Close to Fermi Level

    Homework Statement In class, we discussed metal quantum dots, and we argued that they’re not so useful for device applications since the separation between energy levels for energies near the Fermi energy is much less than a typical optical photon energy of 2 eV. Let’s consider that...
  28. A

    Understanding Density of States in 3d Crystals: A Comprehensive Explanation

    My book gives a treatment of this problem for crystal vibrations, but I don't really understand it. It says: There is one allowed value of K per volume (2\pi/L)3. But at the same time it has just shown that Kx,Ky,Kz can take values ±2\pi/L which would certainly lead to more combinations of...
  29. G

    Infinite Square Well - Particle in linear combination of states

    A particle of mass m is trapped in a one-dimensional infinite square well running from x= -L/2 to L/2. The particle is in a linear combination of its ground state and first excited state such that its expectation value of momentum takes on its largest possible value at t=0.I know the process of...
  30. C

    Infinite energy states for an harmonic oscillator?

    So, I've read conference proceedings and they appear to talk about counter-intuitive it was to create an infinite-energy state for the harmonic oscillator with a normalizable wave function (i.e. a linear combination of eigenstates). How exactly could those even exist in the first place?
  31. M

    Quick question on ensembles of pure states

    Hi folks, I just have a question concerning whether it is possible to produce an ensemble of individual electrons in pure single-particle spin states. I'm assuming it is possible, but sometimes one hears that strictly speaking all electrons are entangled with one another, which would mean...
  32. S

    If problem states acceleration is constant what is the acceleration?

    If problem states "acceleration is constant" what is the acceleration? While gliding down a steep hill, a bike rider experiences constant acceleration. After 4.50 seconds, he reaches a final velocity of 7.50 m/sec. The bike's displacement was 19.0 meters. I know that I'm supposed to be using...
  33. M

    Understanding Spin and Color States in Particle Dynamics

    Hi folks, I was just reading about symmetries, and why we say that the two spin states of the electron are states of the same particle, while we are free to say that the two strong isospin states define tow different types of particle. According to the book I'm reading, we must attribute two...
  34. T

    Normalization of Linear Superposition of ψ States

    Homework Statement An electron in an infinitely deep potential well of thickness 4 angstroms is placed in a linear superposition of the first and third states. What is the frequency of oscillation of the electron probability density?Homework Equations E=hωThe Attempt at a Solution My main...
  35. P

    Rotational exited states spin and parity

    Hi, If you have a even-even nuclei which is deformed, you get a rotational spectrum of 0+,2+,4+,... I don't understand why the parities are positive for even I and why all members of a rotational band must have the same parity. I read about this in Krane's book: an introduction to nuclear...
  36. S

    A question about Qubit (number of states)

    Hi I read this information about the Qubit: "N Qubits are equivalent 2^N classical bits (2^N states)" But I couldn't understand that, because I know that each single Qubit could be one and zero at the same time, so each single Qubit is equivalent two classical bits (two states) That...
  37. camipol89

    Are Thermal States Always Mixed States?

    Hey guys, I was reading about thermal states and now I have a doubt: is a thermal state always a mixed state with density matrix ρ=exp(-βH)/Tr(exp(-βH)), or is there also a pure thermal state? Thank you
  38. J

    Preparing entangled states, how is this possible in the simpest cases?

    I'm having trouble finding comprehensible explanations of how experimenters can ever know that two particles are entangled. I understand that the first experimental confirmation of entanglement used Calcium or Mercury vapor which when excited gave off pairs of entangled photons. But how did...
  39. C

    Fraction of unoccupied electron states

    Homework Statement 2) For an intrinsic (undoped) semiconductor at room temperature with the Fermi energy in the center of the 1 eV band gap, find the fraction of unoccupied electron states at the top of the valence band and the fraction of occupied states at the bottom of the conduction...
  40. R

    Density of States (Condensed Matter)

    Homework Statement I need some help with the following problem: Homework Equations ##\rho(k) dk = \frac{L}{\pi} dk## ##L=Na## ##\omega^2= \omega_m^2 \ sin^2 (qa/2)## The Attempt at a Solution The density of states is given by: ##g(\omega)= \rho (k) / \frac{dw}{dk}## Where...
  41. R

    Conduction Band Density of States for 2D Electron Gas

    For an electron gas generated in the inversion layer of a semiconductor interface, my book gives the conduction band density of states for the two dimensional electron gas as: ##g(E)=\frac{L^2m^*}{\hbar^2 \pi}## Where m* is the effective mass of the electron. I can't follow how this was...
  42. A

    Error in Griffiths QM: completeness of stationary states

    According to Griffiths QM book, after he derived the stationary state solutions to the Schrodinger equation for a particle in an infinite potential well, which are just functions of sine, he claims that these stationary solutions are orthogonal and complete. I agree that they are orthogonal...
  43. S

    Explaining Fermionic Fields & Classical Coherent States

    hi i know what is coherent state, but i read this text in an article and i don't understand this " if we wish to describe long range macroscopic forces, only bosonic fi elds will do, since fermionic fi elds cannot build up classical coherent states. " can you explain it for me, how...
  44. Solarmew

    Understanding Spin States of Particles with Spin-1 and Spin-1/2

    Ok, so for some reason this section of the GRE book makes 0 sense to me ... maybe because i haven't taken the class yet, maybe I'm missing something ... It says "If you have a spin-1 particle with m = +1 and a spin-1/2 particle with m = +1/2, then m_tot = +3/2 (this part makes sense, you just...
  45. M

    Why are entangled states generic?

    Hi folks --- I was just reading that entangled states are very much the norm in the universe. Can anybody tell me why entanglement is taken to be such a pervasive feature of the world, so that product states are the exception? Has it got something to do with the fact that strictly speaking all...
  46. naima

    Are There Only 4 Bell States According to Wikipedia's Definition?

    I look at wikipedia.org/wiki/Bell_state and use the same notations. The article says that there are just 4 Bell states. Is not |\xi^+\rangle = \frac{1}{\sqrt{2}} (|0\rangle_A \otimes |+\rangle_B + |1\rangle_A \otimes |-\rangle_B) another maximally entangled state? The Schmidt decomposition...
  47. M

    Why are interacting states necessarily entangled?

    It just occurred to me that I don't know why composites of interacting particles are always in entangled -- as opposed to mere product -- states. Obviously if they are not interacting we will just represent them as being in a product state; but why is it that being in a product state entails...
  48. nomadreid

    Causation between states or only between measurements?

    In the use of the word "causation" can one say that one quantum state "causes" another if the two states are not measured? Or does the concept of causation only refer to a relationship between measurements?
  49. K

    Calculating transition rate between nljm resolved states

    I know how to calculate transition rates between nl resolved states in a hydrogen-like atom, but I don't know how to calculate transition rates between nljm states. I know that dipole transition rate is \frac{32}{3}\frac{\pi^3 \alpha c}{\lambda^3}\left<\psi_1|\mathbf{d}|\psi_2\right> The...
  50. C

    Can the 'mass' of bound states show up full propagator?

    The result of the Kallen-Lehmann spectral representation is that the two point correlation (and thus also the full propagator) has a pole in the physical mass of the particle. In Peskin and Schroeder it is also argued that multiparticle states show up as a cut, but bound states can also show up...
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