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

    I Bound states of a periodic potential well in one dimension

    Hi, I'm trying to understand the bound states of a periodic potential well in one dimension, as the title suggests. Suppose I have the following potential, V(x) = -A*(cos(w*x)-1). I'm trying to figure out what sort of bound energy eigenstates you'd expect for a potential like this. Specifically...
  2. T

    B Constrained Quantum States: Exploring the Meaning

    What does it mean to say that a quantum state or wavefunction is constrained?
  3. edguy99

    I Can the spin states of a spin1 particle be modeled?

    There is a video from the Space Station here: At around the 1 minute mark, you see the stability of the CD player when the CD inside is spinning. Don Pettit goes on to tape additional CD players together at 90 degrees to the original to make it stable in 2 directions, but my questions is are a...
  4. rocdoc

    I Do I have the correct form for the number of states, the |n>?

    I cannot find any explanation of the mathematical form of the single-mode photon number states, i.e. the |n>. I take them to be functions with domain {0,1,2,3, …} and appropriate associated outputs. So |3> I take to have outputs {0,0,0,1, 0, …} , |0> to have outputs {1,0,0,0, 0, …} and...
  5. Comeback City

    What factors determine an atom's oxidation state?

    I understand the concept of oxidation states and how to find them, but what confuses me is how an atom "decides" which oxidation state to choose. Or even "what it is at all" that decides the oxidation state. Specifically, the transition metals with multiple oxidation states seem to be the...
  6. S

    A A new conjecture on the micro states of black-holes

    Dear All Gravitinos, I write this post here to discuss a new conjecture on resolutions of the schwarzschild singularity and the physics interpretation for the micro states of black-holes (arxiv: 1606.06178, published in Nucl. Phys. B2017,02,005...
  7. bananabandana

    Why are unperturbed states valid basis for perturbed system?

    Homework Statement So we have a two state system, with unperturbed eigenstates ## |\phi_{1}\rangle##, ## |\phi_{2}\rangle ##, and Hamiltonian ## \mathbf{\hat{H_{0}}}## - i.e ##\mathbf{\hat{H_{0}}}|\phi_{1}\rangle = E_{1}|\phi_{1}\rangle## We shine some z-polarized light on the system. This...
  8. T

    Probability of getting specific states -- Quantum Mechanics

    I'm pretty new to quantum, so I'm pretty sure I'm missing something basic here. I've got a 4x4 Hamiltonian with eigenkets $$\psi_{U} = 1/(\sqrt 2) (\psi_{1up} \pm \psi_{2up})$$ and $$\psi_{D} = 1/(\sqrt 2) (\psi_{1down} \pm \psi_{2down})$$ The only difference between the two states is the spin...
  9. Luca_Mantani

    A Invariant combination of SU(3) states

    Hi everyone, this is something i know because i saw it many times, but i have never fully understand it. Suppose i have a quark field (singlet under SU(2) let's say) ##q## and i would like to build an invariant term to write in the Lagrangian. The obvious choice is to write a mass-term...
  10. L

    Fermi energy for two spin states equal in equilibrium?

    Homework Statement Let's consider conduction electrons (at T=0K) that are put in a magnetic field. The electrons can have spin that is parallel or antiparallel to the magnetic field. Below is the density of occupied states for such a system (horizontally) as a function of energy (vertically)...
  11. A

    B Need Listing of Photon and Particle Quantum States

    Hi, I am learning quantum entanglement. I am interested to create an up to date list of all known : - Photon Quantum States - Particle Quantum States - Classically entagled photon states I guess that there is an organization out there that already have this info. If someone can point me into...
  12. C

    Different states of a Carnot Cycle

    Homework Statement A Carnot engine with water as the working fluid operates with a water recirculation rate of 1 kg/s. For TH = 475 K and TC = 300 K, determine: a. The pressure of each state b. The quality of each state c. The rate of heat addition d. The rate of heat...
  13. O

    I Examples where mixed states are eigenstates

    I have actually read so much about density matrix and eigenstates today. I just want to know what particular situations when mixed states are eigenstates. Can this occur? Mixed states and eigenstates have one thing in common.. they have a value.. but I know mixed states aren't eigenstates...
  14. G

    How Many Basic States Exist for Particles in Divided Spaces?

    Homework Statement Four distinguishable particles move freely in a room divided into octants (there are no actual partitions). Let the basic states be given by specifying the octant in which each particle is located. 1. How many basic states are there? 2. The door to this room is opened...
  15. F

    I Are Eigenstates of operators always stationary states?

    Hello everyone, I am wondering if the eigenstates of Hermitian operators, which represent possible wavefunctions representing the system, are always stationary wavefunctions, i.e. the deriving probability distribution function is always time invariant. I would think so since these eigenstates...
  16. T

    I Difference between Quantum Superposition and Mixed States

    Hello, sorry, I do realize that this question has been asked before but there are just a few things I would like to figure out. So, in my mind the differences lie in knowing the states that the system could end up in, and also the difference in the probabilities. Is this thinking correct...
  17. F

    I Two quantum states and qubits....

    Hello everyone, My understanding is that a two-quantum state system is simply a system that can only be in two states. That is equivalent to say that the observable of interest that is being considered can only have possible values. Is that the case? If so, a classical bit can have two values...
  18. M

    I Psi-epistemic arguments against reality of quantum states

    I was just reading a paper <predatory publisher reference deleted> There is an argument (originally by Spekkens), in Section 2.1, that is supposed to be against psi-ontic interpretations. As I understand it, it's that if someone hands you a particle in state x+ or y+ you cannot tell the...
  19. G

    A Paschen notation for electronic states of Argon atom

    Hello. I think excited states of Argon atom is described by j,l coupling written as (2s+1)[K]J. However, when I read some papers describing cross section data for Argon atom, data are quoted with strange notation, Paschen notation. I tried to study the Paschen notation and found that its form...
  20. hilbert2

    A Overlap of Ground States in Quantum Field Theory

    I was reading Peskin&Schroeder's QFT book, and there was some discussion about how ##\left|0\right>##, the ground state of a free field and ##\left|\Omega \right>##, the ground state of an interacting field differ from each other, and they outlined how the latter can be obtained by propagating...
  21. S

    B Energy States: Solid, Liquid, Gas & More?

    Does energy have different states analogous to the solid, liquid, gas, and plasma states of matter? Would they be the same as "forms of energy" described here? https://en.m.wikipedia.org/wiki/Forms_of_energy
  22. Kara386

    Calculating 3D Density of States for a Dispersion Relation | Homework Solution

    Homework Statement Calculate the single-particle density of states ##g(\epsilon)## for the dispersion relation ##\epsilon(k) = ak^{\frac{3}{2}}## in 3D. Use ##g(k) = \frac{Vk^2}{2\pi^2}##. Homework EquationsThe Attempt at a Solution This question is worth lots of marks. My solution is a few...
  23. G

    System simplification through state space

    Hi guys! I study Electrical Engineering and, don't-know-why, I don't know anything about state space. Now I'm working on a project where I have a non-linear system. The first task in the project is to separate the linear and the non-linear part of this system, and then obtain the state space...
  24. petrushkagoogol

    Behavior of charged particles in Free and Bound states

    If there are 3 positive charges of +1, +3, +5 coulombs equidistant from a negative charge of 1 coulomb what positive charge will this negative charge be attracted to ? Is the result different if the charges exist in a “bound” state (resulting in electrovalent compounds) where a positive charge...
  25. G

    Kalman Filter States: What Do They Represent?

    It will sound a little bit stupid, but Ill ask anyways: I have two series systems, the second is an UKF (Uscented Kalman Filter). I was told to reduce the first system in order to that the UKF estimate less states. My question is: What exactly do the states represent? I mean, if I have a...
  26. A

    I What k states are occupied in a band

    In solid state physics you can calculate the band structure of a material, which is effectively the dispersion E_n(k), which depends on the wavevector as well as the band index. What I don't understand is this: Which states are occupied in a band? With this I mean: Which k values correspond to...
  27. C

    B States as positive operators of unit trace

    I read that states are positive operators of unit trace - not elements of a vector space. Is it referring to quantum states or all classical states? I know operators are like minus, plus, square root and vectors are like rays in Hilbert space.. but why can't quantum states be vectors when in...
  28. Konte

    I Stationary states -- Boltzmann distribution

    Hello everybody, - In quantum mechanics, the state ## | \psi \rangle ## of a system that is in thermodynamic equilibrium can be expressed as a linear combination of its stationary states ## | \phi _n \rangle ## : $$ | \psi \rangle = \sum_n c_n | \phi _n \rangle $$ It permit us to express the...
  29. M

    I Two single-photon Fock states vs one two-photon Fock state

    What is the difference between two single-photon Fock states ##|1\rangle |1\rangle## and one two-photon Fock state ##|2\rangle## (all in the same mode)? In both cases the mean photon number is 2. How do we distinguish them experimentally?
  30. Mayan Fung

    B Quantum Oscillator States: Is the Ladder Operator Enough?

    We learned that we can use the ladder operator to obtain the states of a quantum oscillator. However, I see no direct evidence to show that the solutions are complete. I mean, how can we know the energy state follows E is (E+hw). Why can't we have some more states in between? Does the derivation...
  31. SWFvanRijk

    A Are Mesons in Colour Singlet State?

    I read that hadrons are in colour singlet state and that gluons are not and that the colour singlet gluon is forbidden for the reason of making strong force a long range force otherwise (and that SU(3) has 8 generators and thus 8 gluons) but my question is: are mesons in a colour singlet state...
  32. A. Neumaier

    A States in relativistic quantum field theory

    No. This is a noncovariant, observer-specific view.In the covariant, observer-independent view of fields, states are labeled instead by the causal classical solutions of hyperbolic field equations. On the collection of these the Peierls bracket is defined, which is the covariant version of the...
  33. Nosebgr

    Overlap of two spin one-half states.

    Homework Statement Consider a spin state |n; +> where n is the unit vector defined by the polar and azimuthal angles θ and φ and the spin state |n'; +> where n' is the unit vector defined by the polar and azimuthal angles θ' and φ'. Let γ denote the angle between the vectors n and n': n⋅n' =...
  34. K

    I Maximally entangled two-qubit Bell states

    Hello, In the four maximally entangled two-qubit Bell states, what is the difference between the first and the second states, similarly, the difference between the third and the fourth states. What the different in signs mean( +,-)...
  35. t_r_theta_phi

    B Difference between opposite states

    Let's say there are two 1/2 spin particles, one in state 1/√2 |up> + 1/√2 |down> and the other in the state - 1/√2 |up> - 1/√2 |down> Both particles then have an equal chance of being measured to be in either the up or down states. Is there any physical difference between these or are they...
  36. P

    I States diagonal in the reference basis

    Hello, can someone give an example for an incoherent State --> a formula is here on page 7 : http://quantumcorrelations.weebly.com/uploads/6/6/5/5/6655648/2016_robustnessofcoherencetalk.pdf I know that coherenc is e.g. a superposition of e.g. Spin-Up and Spin-Down [z] or so... But i have no...
  37. H

    I Why do Hydrogen bound states span the Hilbert space?

    As the title says, why does the set of hydrogen bound states form an orthonormal basis? This is clearly not true in general since some potentials (such as the finite square well and reversed gaussian) only admit a finite number of bound states.
  38. E

    B Measuring Hardness of Substrates in Changed States

    Just wondering, if an experiment had ever been conducted to measure hardness of a substrate when it was in a changed state. MOHs law measure products when they were at room temperature (although I guess temperature was never really a consideration). So what would be the MOH's hardness of ice...
  39. Chenyb

    A Is the Quantum State in a Dressed Atom System Pure?

    Consider a simple two level atom system,|1>,|2> (not degenerate) interacted with monochromatic laser, of which the frequency is exactly resonant with the |1> to |2> transition. The evolution start from {1>. As far as I understand, the dressed degenerate state |1>|n> and |2>|n-1> will get...
  40. A

    I Density of states at Fermi level for metal vs semiconductor

    We are doing spectroscopy on some semiconductors covered by a layer of Aluminium. My professor says it might be a challenge for to see the valence band structure of the semiconductor because the metal has a high density of states at the fermi level. Does this make sense to you? Does a metal have...
  41. woody stanford

    I How does a single photon camera pixel work?

    Here is an interesting article off of phys.org that I really liked. http://phys.org/news/2012-08-caught-camera-quantum-mechanics-action.html What I found interesting is its premise of visually capturing multiple quantum states so that one could personally inspect a lot of these issues that...
  42. evinda

    MHB Find DFA Equiv: States, Transitions & Function

    Hello! (Wave) I want to find a DFA equivalent with the following: Do we have to follow the following procedure? If so do we have to find the transition function having the following states? $$\{A\} , \{ B \}, \{ C \}, \{ A,B \}, \{ A,C \}, \{ B,C \}, \{A,B,C\}$$
  43. V

    I Confusion about initial states and coherent states

    I've found online that the coherent state of the harmonic oscillator is |\alpha \rangle = c \sum_{n=0}^\infty \frac{\alpha^n}{\sqrt{n!}} | n\rangle where |n\rangle = \frac{(a^\dagger)^n}{\sqrt{n!}} |0\rangle and |0> is called the initial state. I've some code where I need to have this...
  44. B

    B Are Pointer States Primitives in Quantum Mechanics?

    Someday if there are experiments that can show it.. it's still a possibility that in Quantum Darwinism or Everettian, pointer states are primitives? This means if there are no pointer states. The universe won't be classical at all. Because there are arguments that they have to conform to...
  45. Q

    I Interpret Heisenberg Picture: Operators & States

    Can anybody give a natural interpretation of operators and states in the Heisenberg Picture? When I imagine particles flying through space, it seems that the properties of the particles are changing, rather than the position property itself. Is there any way I should be thinking about these...
  46. T

    I Finding probability of changing states

    I am following the derivation shown in this link on adiabatic passage. I have posted one part below: I am simply wondering how this expression was derived and how it indicates the probability of being in a state that is different from the initial state? How exactly is this represented by...
  47. H

    B Still confused about superposition and mixed states

    I am confused about pure state or in mixed states. I've seen several threads on this forum, but I still can't get the grasp of it. I only have very little quantum chemistry to know what these means. So instead, I want to know the answer for specific examples so that I can get an idea. So I...
  48. 1

    I Why do we calculate the density of states using k-space?

    In statistical physics the calculation to obtain the density of states function seems to involve an integral over an eighth of a sphere in k-space. But why do we bother moving from n-space to k-space, if there's a linear relation between n and k i.e. n = (L/π)k ? Why don't we just integrate over...
  49. hilbert2

    A QFT and transitions between momentum states

    Hi, I'm trying to learn some QFT at the moment, and I'm trying to understand how interactions/nonlinearities are handled with perturbation theory. I started by constructing a classical mechanical analogue, where I have a set of three coupled oscillators with a small nonlinearity added. The...
  50. D

    I What is the Eigenvalue of Coherent States?

    Hi. I don't understand what is meant by the eigenvalue α of a coherent state where a | α > = α | α >. The eigenket |α > is an infinite superposition of the number states , ie | α > = ∑ cn | n > and for each number state a | n > = √n | n-1 >. So for each number state the eigenvalue of the...
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