States Definition and 1000 Threads

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. C

    Differential Equation with 4 states

    Dear Physics Forums, I have a reaction scheme with 4 states where A<->B, B<->C and B<->D: C / A - B \ D This proceeds to equilibrium from a start point of A = 1 and B, C, D = 0. Forward and reverse rate constants for A<->B are K(1) and K(-1), for BC...
  2. S

    The single particle density of states (Statistical physics)

    Homework Statement I'm having a little bit of trouble getting started with this problem. Can I get a little help? Using: (number of states in the six-dimensional region d^{3}x d^{3}3p) = (d^{3}x d^{3}p)/h^{3} Which provides a convenient route to the single-particle density of masses. a)...
  3. P

    Coherent states of a Quantum Harmonic Oscillator

    Homework Statement Given that a^+|n\rangle=\sqrt{n+1}|n+1\rangle a|n\rangle=\sqrt{n}|n-1\rangle and that the other eigenstates |n> are given by |n\rangle=\frac{(a^+)^n}{\sqrt{n!}}|0\rangle where |0> is the lowest eigenstate. Define for each complex number z the coherent state...
  4. D

    Calculated Density of states (DOS)

    Hello! I have a very simple question... Does anyone know if exists on the WWW a database where I can download the calculated density of states for the transition metals? I want data not just pictures! Thanks
  5. R

    Rydberg States Exhibiting Quantum Defect?

    I am posting this to see if any readers/mentors, etc. can refer me to any type of reference for Rydberg states that also exhibit the quantum defect wherein we need to be concerned with the attractive force between the nucleus (or possibly, the ion core) and valence electrons as the penetration...
  6. J

    Mixed states and pure states: what's the difference?

    Hi, this is probably a straightforward question over something simple but it's confusing me. I don't get what the difference is between a mixed state, a superposition and a pure state. I'm looking through my notes about density operators and it's talking about a qubit system where |0> =...
  7. L

    Why do solids stay hotter longer than other states?

    Does it have to do with the fact that the molecules vibrate so close to each other, and transfer more energy to each other?
  8. Y

    Energy of a QM system, stationary states

    I'm pretty confused by the rules regarding the total energy, the kinetic energy, and potential of a QM system. Does the total energy have to be positive or greater than zero? And if so, why not? I don't really understand what it means to have a negative total energy of a system I guess. I...
  9. N

    Two-particle fermionic basis states

    Hi guys Say we are looking at a two-particle system consisting of two electrons (fermions). In my book it says that the basis states are given by \left| {\psi _{\alpha ,i} (r_m )} \right\rangle \left| {\psi _{\beta ,j} (r_n )} \right\rangle where rm and rn denote the two particles...
  10. O

    Photon Emission and Energy Levels in a Hydrogen Atom

    Homework Statement A hydrogen atom is excited from the state with n=1 to that with n=4. Calculate the energy (in eV) that must be absorbed by the atom. Calculate and display on an energy-level diagram the different photon energied (in eV) that may be emitted in order for the atom to reach...
  11. E

    Uncontrollable States in State Space

    Hi Guys/Gals If you end up with a row of zeros in the controllability matrix for a linear state space system, does that row correspond with the state that is uncontrollable eg. Assuming a linear state space system with 5 states, a row of zeros in the 4th row of the controllability matrix...
  12. N

    Unique Eigenvector of a: Unveiling Coherent States

    Homework Statement Show that, for all complexe numbers \alpha, a has a unique eigenvector |\alpha\rangle that is nothing else but the coherent state \psi(x)=\frac{e^{-\frac{i}{2\hbar}\langle X\rangle\langle P\rangle}}{(\pi\ell^2)^{1/4}}e^{-\frac{(X-\langle...
  13. J

    Which Electron Transitions in Singly-Ionized Helium Emit Blue Light?

    Which electron transitions in singly-ionized Helium (He+) yield photons in the blue (450-500 nm) portion of the electromagnetic spectrum? What are their wavelengths, and what transitions do they represent? Homework Equations hear is the equation I tried to use an equation creator but did not...
  14. T

    Superposition of states and orthonormalization

    Homework Statement Consider a particle in a superposition of states given at time t=0 by Y(x,0)=C(y1(x)+y2(x)), where y1(x) and y2(x) are the stationary states with energies E1 and E2 respectively. if y1(x) and y2(x) are orthonormalized, what value of C is required to normalize Y(x,0)...
  15. H

    Find Logic Classes in the US: Course Code & Info

    I would really like to take a logic class, but I can only find philosophy classes that have logic. Have you ever taken a logic class with philosophy? If so, did it cover logic exhaustively? Do you know if there are any classes that have logic solely? If so, what was the course code for that...
  16. D

    How Can a Sensor Detect Green LED States?

    I'm doing a project where I need a sensor to monitor a standard green LED and determine if it is ON, OFF, or BLINKING. I have been considering using a phototransistor or photodiode, but I am not sure how I would use one of these to tell the difference in the LED being on or blinking. Does...
  17. M

    How Does Time-Dependent Perturbation Impact Electron Spin State Evolution?

    Hello All, Using Time dependent perterbation we could predict the Rabi precession and the spin states of the electrons, for example, in an external magnetic field. I was wondering how could we calculate the evolution from a random spin state to one of the defined spin states, does it defy the...
  18. T

    Path integral in coherent states

    Hey, there is something I don't really understand about the path integral (functional integral) formalism in QFT: Why do you need to introduce a coherent-state representation of the Dirac fields in order to evaluate their path integral? Where is the crucial point why it doesn't work like...
  19. kreil

    Quantum Mechanics pure/unpure states

    Homework Statement It is shown in the following two equations that any nonpure state operator can be decomposed into a mixture of pure states in at least two ways. Show, by constructing an example depending on a continuous parameter, that this can be done in infinitely many ways.Homework...
  20. N

    Exploring Quantum States: Bell vs. Total Spin

    Towards the end of http://www.youtube.com/watch?v=IAgV-LKTiMI&feature=channel" video at 54:55, the professor defines the four possible states of two entagled electrons as follows: singlet |0,0> = |u,d> - |d,u> triplet |1,1> = |u,u> |1,0> = |u,d> +...
  21. B

    Quantum physics- atomic states

    Homework Statement Give the full designation (e.g. 3P0) for all possible singlet, doublet, triplet and quartet S, P and D atomic states. The Attempt at a Solution I don't understand this question at all! Up to which values does the angular momentum (supscript) and multiplicity...
  22. H

    Expectation value of momentum in discrete states

    Is there any way of proving <p> = 0 for a discrete (bound) state given it's wave function? I've seen proofs using the hermitian properties of p but I'm interested in proving that the integral of Psi*(x) Psi'(x) is identically zero regardless of Psi(x) as long as it's a solution of Schroedinger's...
  23. S

    Principle stress states question, anyone help?

    Principle stress states question, anyone help?? Homework Statement Neutron diffraction is used to measure the residual strains near to a weld in an aluminium plate. The aluminium has a young’s modulus E of 70GPa and a poisons ratio of 0.3. The three principal strains obtained are ε1= 2400 με...
  24. S

    Understanding Mixed States, Pure States

    This question is from an example taken from Zurek 1991 (Decoherence and the Transition from Quantum to Classical). Start with a spin state of an electron, \Psi= a|+> + b|-> Question 1: Why is this considered a pure state? I figured it would not be called "pure" since it is a superposition...
  25. S

    Schools Physics PhD programme in the states, what Universities to go for

    I would like some advise about what universities to apply to in the states for PhD programmes in physics. In particular what level of university (as defined by school rankings etc). I've been told that the high end universities can be overly stressful and that they foster a highly competitive...
  26. S

    From Heisenberg to Superposition states

    Hi All, I am trying to remember the logical argument that leads from Heisenberg's uncertainty principle to the existence of quantum superposition states. Here's my sketchy version: 1) postulate of Quantization leads to non-commuting operators 2) This leads to Heisenberg Unc. Principle...
  27. C

    Do we know for sure if gravity exists in quantum states?

    I was just wondering because it seems there is a contradiction in qm. If a quantum state can only be represented by an abstract statistic then would not gravity be equally subjective until decoherence occurs? And what about entanglement? It appears to act as a constant (an immediate one)...
  28. W

    Effing Virtual States - How do they work?

    Effing Virtual States -- How do they work? I want to talk to a scientist because this is pissing me off. >:-( So, I'm learning about CARS and Raman spectroscopy. Since Day 1 of Modern Physics I've been told that atoms have discrete energy levels and only the only way to get an electron from...
  29. M

    Why do probabilities distinguish between multiplet states?

    I'm pretty sure the answer to this will be more than obvious, but I've been wondering about the following. Isospin invariance is assumed to be an (approximate) symmetry of the strong interactions. Ratios of cross sections for strong interactions are then given by the appropriate SU(2)...
  30. U

    States of a spin 1/2 particle in a magnetic field

    Hi, for my quantum mechanics course I'm confronted with the following question: Homework Statement A spin 1/2 particle has the following eigenstates of Sz: |+> = (1 0) and |-> = (0 1). A magnetic field is pointing in the z direction, B = (0,0,B). The Hamiltonian is H = -B * n, with n =...
  31. D

    The Illusion of the Future: Equal Existence of All States

    Imagine viewing the world from state X at 1 pm, and viewing the world from state Y at 2 pm. State Y is required to be in existence in principle at the viewing of state Y, and at state X equally. This is because neither is more valid of a state to view the world from. Neither can claim it is more...
  32. X

    Solving Density of States Problems in Molecular Quantum Electro Dynamics

    Dear all, I am doing summer research in the field of Molecular Quantum Electro Dynamics, and a persistent problem that I (and occasionally the group I am working with) have/has is knowing what to use as the density of final states (radiation states). It is required in the Fermi Golden...
  33. M

    Density of States Homework: Show $\rho=Vk^{2}/\pi^{2}$

    Homework Statement According to the non-relativistic quantum mechanics of a particle of mass m in a cubic box ov volume V = L3, the single particle energy levels are given by Ek=\hbar2k2/2m where k is the magnitude of the wavevector K = (kx,ky,kz) and where the components of k are...
  34. MTd2

    Particles as different states of a matter field.

    This is too wild to post on beyond standard model but I am not proposing anything here. Just want to know your thoughts. Is it reasonably possible to conceive particles as solitons corresponding to metastable states of a unique universal matter field?
  35. A

    Calculate the energies of the six lowest states

    Homework Statement Suppose that a particle of mass m is confined to move in the x-y plane in a 2-dimensional box of length Lx = L and LY = ½ L. Calculate the energies of the six lowest states. Homework Equations not sure to set up this problem? The Attempt at a Solution the most...
  36. L

    How do we calculate spin functions and determine singlet and triplet states?

    Hi there, I would be most grateful if someone would explain how do we calculate the spin function χ(s_1,s_2 )=1/√2 [α(s_1 )β(s_2 )±α(s_2 )β(s_1 )] both the symmetric and antisymmetric α(s_1 )β(s_2 )+α(s_2 )β(s_1 ) = ? α(s_1 )β(s_2 )-α(s_2 )β(s_1 ) = ? knowing that α( + 1 / 2) = β(...
  37. M

    How Does Observed Superposition Impact Interpretations of Quantum Mechanics?

    Since there have now been directly observed superpositions in laboratory experiments, meaning of course that superposition is not an interpretative issue but an observed aspect of nature, does this have any consequences for certain interpretations of QM? I particurlarly had in mind hidden...
  38. J

    What is the Trace of Density of States?

    regarding the density of states: how I GET THE FOLLOWING EQUALITY? \langle E_n\mid \delta(E-\widehat{H}) \mid E_n \rangle = \sum_n \delta(E-E_n)
  39. P

    Deriving DOS of Bilayer Graphene Under Electric Field

    Hi all. Is there any place where I can check how to derive the DOS of bilayer graphene subject to an external field. I have got the Hamiltonian right and solved the eenrgies but then I am not sure how to obtain the DOS right.. Thanks
  40. M

    Transition metal oxidation states

    Hi Why does Ni only form NiO with oxidation state of +2 whereas the other transition metals form a wide range of oxides with variable oxidation states Thanks
  41. A

    Transition states of electron in atom

    as we know when a particular energy is given to a neutral atom an electron from ground state jump to upper state (absorbing the energy). and that excited electron after sometime by releasing energy jump again to its ground state. my confusion is that firstly does this transition of electron...
  42. W

    Why two s=1/2 states can be linked by a rotation, but not two s=1 states?

    given two arbitrary states of a spin of 1/2 we can always find a rotation to link these two states however, given two arbitrary states of a spin of 1 this is not so for example, (0,1,0) and (1,0,0) can not be linked by a rotation the former has vanishing expectations of sx, sy, sz so in...
  43. K

    How Do You Determine Spin States from a Hamiltonian?

    Sorry if this question is very general/vague, but I would prefer a general answer rather than a specific solution... I'll put more detail in if necessary though. So, say we have a Hamiltonian for a system (of fermions, spin 1/2); then we find its eigenvalues and hence eigenstates. These are...
  44. O

    Displacement operator for coherent states?

    Hi everyone, I have the following question about coherent states: It is known that the creation operator has no eigenket. However, the action of a creation operator a^{\dagger} on a coherent ket |\alpha\rangle can be written as a^{\dagger}|\alpha\rangle = \left( \frac{\partial}{\partial...
  45. B

    Stationary States and Spreading of Wave Function

    What I know: In stationary states the time dependence is factored out so it is of the form phi(q) * e^(-i omega t), thus in its appearance there is no wave function spread. However I recall from texts that wave packet spread is considered a universal phenomena in quantum mechanics, so I am...
  46. L

    What do the 4 spin states of two particles represent

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  47. tom.stoer

    L² Hilbert space, bound states, asymptotics of wave functions

    Hi, I asked this question in the quantum physics forum https://www.physicsforums.com/showthread.php?t=406171 but (afaics) we could not figure out a proof. Let me start with a description of the problem in quantum mechanical terms and then try to translate it into a more rigorous mathematical...
  48. M

    Oxidation states of manganese and pH

    Hi I am interested in the change in the stability of the oxidation states of manganese with pH Mn is a stronger oxidising agent in acid than in base which would lead you to believe that the higher oxidation states of Mn are more stable in alkaline conditions. Does anyone have a reason...
  49. tom.stoer

    L² Hilbert space, bound states, asymptotics of wave functions

    Hi, I discussed this with some friends but we could not figure out a proof. Usually when considering bound states of the Schrödinger equation of a given potential V(x) one assumes that the wave function converges to zero for large x. One could argue that this is due to the requirement...
  50. dextercioby

    Hybridization states of the 8 orbitals (*) of Xe and Os

    Dear all, can you point me to a book reference where the hybridization states of the 8 orbitals (*) of Xe and Os in these 2 compounds \mbox{XeF_{8}} and \mbox{OsF_{8}} are justified in agreement with the quantum theory? Do these 16 bonds involve the "f" orbitals or not ? Thank you...
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