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. mcastillo356

    Calculus Where did my textbook say clearly what it states at this point?

    Hi, PF I left reading for a while, and now I must revisit a quote from Spanish 6th edition of "Calculus", by Robert A. Adams. The quote is " 4.2 Extreme values problems (...) As we've seen, the sign of ##f'## shows if ##f## is increasing or decreasing". Obvious, I shouldn't care and...
  2. D

    B Irreversible Process to Move Gas from State 1 to State 2

    Summary:: Irreversible process required to go from state 1 to state 2 If we start with an ideal gas at state 1 and undergo an isentropic compression, then follow this with an isothermal expansion, we could end up in a state, call it state 2, that has higher temperature, higher pressure, and...
  3. S

    I Explaining Quantum States: Global Phase

    I was teaching the basics of quantum states and was showing the students that an arbitrary state in a quantum two-level system could be written as ##|\psi\rangle = C_1 |+\rangle + C_2 |-\rangle = R_1 |+\rangle + R_2 e^{i \alpha} |-\rangle##, with {##C_i##} complex and {##R_i##} real. Then...
  4. D

    A Fidelity between initial and final states

    I have a state |0>|alpha>. Now I want to evolve this state at any time t and find the fidelity between the initial and final states. Any ideas how to do that? My main problem is that I don't know how to evolve this state.
  5. BigMax

    I The Meaning of Basis States in Quantum Mechanics

    Hi everyone! I've been studying quantum mechanics for a while but I have a big big problem. If a system is in an eigenstate of energy (I use the eigenstate as a basis) it remains in this state forever. But if I describe the system with a different set of basis states (not eigenstates) the...
  6. D

    I Schrodinger Cat states in terms of Displacement Operator

    The coherent state can be written in terms of e^(αb†+α∗b)|0>. But how the even coherent state i.e. |α>+|-α> can be written in terms of displacement operator?
  7. K

    I Dipole moment of Rydberg states

    Hello! Are there any experimental measurements or theoretical calculations of the electric dipole moment of any Rydberg state for CaF or BaF? Thank you!
  8. P

    Iron Oxidation States: Fe+2, Fe+3 & Fe- Explained

    I saw on Wikipedia that Fe has both positive and negative oxidation states. I know that Fe will willingly give up its 2 electrons to form an ionic bond with O for example, making it Fe+2. 1. But how can Fe+3 exist? This means it gives up three electrons right? Does this mean the Fe atoms...
  9. MichPod

    A Does the quantum space of states have countable or uncountable basis?

    It's probably more kind of math question. I consider a wave function of a harmonic oscillator, i.e. a particle in a parabolic well of potential. We know that the Hamiltonian is a Hermitian operator, and so its eigenstates constitute a full basis in the Hilbert space of the wave function states...
  10. patric44

    What is the number of confined states in these potential wells?

    hi guys i came across this question about the maximum and minimum number of bound states that can be confined in these potential wells 1- infinite potential well 2- semi infinite potential well (from one side) 3 - finite potential well i think i have a good idea about the minimum number of...
  11. M

    I What happens to atoms in far detuned states?

    Hello! Assuming we have a 2 level system interacting with an EM field in the RWA and dipole approximation, we would have in the basis of the 2 unperturbed atomic states a 2x2 Hamiltonian matrix with off-diagonal terms. By diagonalizing this Hamiltonian we obtain dressed states which are the...
  12. Andrei0408

    How to find the voltage threshold at which diode switches states?

    I've attached pictures with the circuit and part of the attempted solution. I've replaced the diode with its offset model and obtained the equivalent circuit in the 2nd picture. After applying KVL, I've obtained that u_l=−u_D−i_D*R. Since U_D0 is greater than 0, I've deduced that the diode must...
  13. I

    I Mixed states from entangled state

    I'm an undergrad in physics, and have been asking myself the following question recently. Suppose you have a pure quantum state p (von neumann entropy=0), made of 2 sub-states p1 and p2 that are entangled. Because they are entangled, p \neq p1 x p2. Hence the entanglement entropy of p (=0) is...
  14. L

    Delta potential problem - bound states problem

    I am confused here. For ##x>0## particle is free and for ##x<0## particle is free. That I am not sure how we can have bond states. If particle is in the area ##x>0## why it feel ##\delta## - potential at ##x=0##. Besides that, I know how to solve problem. But I am confused about this. If we...
  15. B

    I Probe absorption and dressed states

    Hello! I am reading about dressed states, and I am presented a situation in which we have a laser (the pump laser) on resonance with a 2 level (atomic) transition, and a second, weak laser (probe laser) that is scanned over a frequency range. The absorption spectrum of the probe laser, for...
  16. L

    I Double delta potential -- Degeneracy of bound states in one dimension?

    I have a question from the youtube lecture That part starts after 42 minutes and 47 seconds. Balakrishnan said that if delta barriers are very distant (largely separated) then we have degeneracy. I do not understand how this is possible when in 1d problems there is no degeneracy for bond states.
  17. patric44

    Derivation of the density of states?

    hi guys i have a question about the derivation of the density of states , after solving the Schrodinger equation in the 3d potential box and using the boundary conditions ... etc we came to the conclusion that the quantum state occupy a volume of ##\frac{\pi^{3}}{V_{T}}## in k space and to...
  18. A

    A Superconductor in a hollow cylinder -- two different end states. Why?

    When a magnetic field is applied to a SC during cool down, the field goes through the hole of the hollow cylinder. When the cool down first takes place and then later a magnetic field is applied, the magnetic field does not go through the hole of the hollow cylinder but rather is expelled to the...
  19. B

    I Confused about dressed states of atom

    Hello! Assume we have a 2 level system, with the ground state defined as the zero energy level and the excited state having an energy of ##\omega_0##. If we apply an oscillating electric field (assume dipole approximation and rotating wave approximation) of frequency ##\omega##, we have a time...
  20. lelouch_v1

    I How to work in the |F,m_F> states in hyperfine structure

    Suppose that we have two atoms with one proton one electron each, and these electrons interact with each other. The states for the electrons are the singlet(S=0) and the triplet states(S=1). My question is if i have to keep the nuclear spin of the protons parallel when i write the states, for...
  21. Jamister

    A Heisenberg Uncertainty Relation for mixed states

    How do you prove Heisenberg uncertainty relations for mixed states (density matrix), only from knowing the relation is true for pure states?
  22. docnet

    Spherically symmetric states in the hydrogen atom

    The equation $$\frac{\hbar^2}{2m}\frac{d^2u}{dr^2}-\frac{Ze^2}{r}u=Eu$$ gives the schrodinger equation for the spherically symmetric functions ##u=r\psi## for a hydrogen-like atom. In this equation, substitute an assumed solution of the form ##u(r)=(Ar+Br^2)e^{-br}## and hence find the values...
  23. Danny Boy

    A Entanglement Witnesses close to GHZ states

    Consider page 2 of Toth's paper Entanglement detection in the stabilizer formalism (2005) . To detect entanglement close to GHZ states, they construct entanglement witnesses of the form $$\mathcal{W} := c_0 I - \tilde{S}_{k}^{(GHZ_N)} - \tilde{S}_{l}^{(GHZ_N)},$$ where...
  24. A

    I Change of variables in the Density of States function

    I have a problem where I am given the density of states for a Fermion gas in terms of momentum: ##D(p)dp##. I need to express it in terms of the energy of the energy levels, ##D(\varepsilon)d\varepsilon##, knowing that the gas is relativistic and thus ##\varepsilon=cp##. Replacing ##p## by...
  25. jk22

    I Can a State with Nonmeasurable Local Properties be Described by Quantum Rules?

    If the state considered is :##\frac{1}{\sqrt{2}}\left[\left(\begin{array}{c}1\\0\\0\end{array}\right)\left(\begin{array}{c}0\\1\end{array}\right)-\left(\begin{array}{c}1\\0 \end{array}\right)\left(\begin{array}{c}0\\0\\1\end{array}\right)\right]## It seems to me it were not locally measurable...
  26. K

    A linear combination of states that diagonalize the Hamiltonian

    He told me I "need to show that the Hamiltonian matrix elements you get by using those states have nonzero elements only on the diagonal." I understand what and how a diagonal matrix works, but what I don't understand is what those states are. Are they states I put in my "quantum mechanical...
  27. Mayan Fung

    I Discreteness of bound vs unbound states

    I observe that all bound states have discrete energy levels, eg. particle in a box, hydrogen atoms. But unbound states always have a continuous energy spectrum. For example, for the case of a finite potential well, when ##E<V_0##, we have discrete energy for the bound states. When ##E>V_0##, the...
  28. Eric Recchia

    In Canada, 80% is an A-, in the States, it's a B-. Does that mean....

    Summary:: Comparing education systems from different countries. ..our education system is easier? Or does that mean our material is tougher and the grading system balances out? Or is just cultural differences. The only exception is York. It doesn't like (-) so an 80 is just an A. 90+ is an A+.
  29. JD_PM

    Modifying photon states to get a gauge symmetry

    I see that this procedure helps to get rid of the two extra degrees of freedom (due to the scalar and longitudinal photons) one firstly encounters while writing the electromagnetic field theory in a Lorentz-covariant way; it indeed shows that modifying the allowed admixtures of longitudinal and...
  30. R

    B How to differentiate b/w two collapsed values in Bell States

    Given the Bell State in Z basis ##\psi = (a\uparrow \downarrow - b\downarrow \uparrow )## where ##a^2+b^2=1##. Now Alice has one particle and sends the other to Bob. Suppose Alice decides to measure her particle in Z direction. Thus entanglement collapses. Query: 1. How do we know which...
  31. AidenPearce

    B When are particles in a superposition of states?

    Hi guys, I hope you all are doing great. If we take the double slit experiment for instance, before measurement particles are in a superposition of states. Once they are "measured", or non arbitrarily interfered with, their wave function collapses and only one state remains. So my question is...
  32. M

    MHB Calculating Steady States: Exploring the "Two Cases

    I've got this question here, I know to calculate steady states you set dn/dT and dc/dT to 0 and then solve. However can anyone help me understand what it means by the "two cases" and how you go about this?
  33. M

    MHB Calculating Steady States: A Guide

    Anyone able to calculate the steady states?
  34. M

    A Clarifying question about surface states

    Recently, I was giving a presentation for my research group related to ARPES to improve my understanding. I mentioned that the probing depth of ARPES is a few angstroms, meaning we can only look at surface states, and I was sort of giving a real space picture. In other words, ARPES can only...
  35. Luke_Mtt

    I Calculate a spin state as a function of the base spin states

    Practically it is said that, given two spin states |u⟩ (up) and |d⟩ (down) - which are the spin measured along the +z and -z semiaxes - such that they are orthogonal ( ⟨u|d⟩ = ⟨d|u⟩ = 0), it is possible to write any other spin states using a linear combination of these two (because they are a...
  36. P

    I Prove that the norm squared of a superposition of two states is +ve

    This is what I have so far: $$ |\alpha\Psi_1 + \beta\Psi_2|^2 = |\alpha|^2|\Psi_1|^2 + |\beta|^2|\Psi_2|^2 + \alpha^*\beta\Psi_1^*\Psi_2 + \alpha\beta^*\Psi_1\Psi_2^* $$ $$=> |\alpha\Psi_1 + \beta\Psi_2|^2 = |\alpha|^2|\Psi_1|^2 + |\beta|^2|\Psi_2|^2 + 2Re(\alpha^*\beta\Psi_1^*\Psi_2) $$ I am...
  37. JD_PM

    Quantum Optics Question Involving Coherent States

    I've tried to square and compare ##\Delta X## and ##\Delta P## but they are not equal I have to say I am pretty lost here and a hint would be appreciated. I have studied coherent states and I know how to proof some properties related to it. For instance, I see how to proof that the state is...
  38. M

    I Normal order and overlap of states

    I have trouble understanding the solution to a homework problem. Consider the interaction Lagragian ##\mathcal{L}_{\rm int} = -iqA_\mu \bar{\psi}\gamma^\mu \psi##, i.e. photon-electron/positron interaction. We want to focus on the Compton scattering $$e^-(\vec p_1, \alpha) + \gamma(\vec p_2...
  39. Kaguro

    Minimum time between two orthogonal states

    E = (1/√2)^2(E1) + (1/√2)^2(E2) = (E1+E2)/2 Let ψ(x,t=0) = ψ0 So, ψ1 = ψ0*exp(-i*E*T1/ħ) and, ψ2 = ψ0*exp(-i*E*T2/ħ) Given, <ψ1|ψ0> = <ψ2|ψ0> = 0 So, <ψ0*exp(-i*E*T1/ħ)|ψ0> = 0 => exp(i*E*T1/ħ)<ψ0|ψ0> = 0 => exp(i*E*T1/ħ) = 0 Similarly, exp(i*E*T2/ħ) = 0 So, exp(i*E*T1/ħ) = exp(i*E*T2/ħ)...
  40. tanaygupta2000

    What is the correct formula for the density of states in 2D for normal atoms?

    For getting the density of states formula for photons, we simply multiply the density of states for atoms by 2 (due to two spins of photons). I am getting the 2D density of states formula as :- g(p)dp = 2πApdp/h^2 I think this is the formula for normal particles, and so for photons I need to...
  41. S

    I Do all mental states really exist in some universe in Many-Minds?

    According to the Many Minds interpretation of quantum mechanics (https://en.wikipedia.org/wiki/Many-minds_interpretation), the distinction between worlds in the Many Worlds interpretation should be made at the level of the mind of an individual observer. I have read that, in this case, each...
  42. P

    A Question: Unambiguous discrimination between two non-orthogonal states

    Consider a VCSEL laser that emits photon pulses with Poisson distribution for the number of photons per pulse. The power of the VCSEL has been set low so the mean photon number "u" is u<1. Consider this photon pulses can take two non-orthogonal states of polarization (for example: state 0 with...
  43. Ishika_96_sparkles

    I Feynman's Lectures volume III (Ch:8) -- Resolution of vector states

    In the section 8-2 dealing with resolving the state vectors, we learn that |\phi \rangle =\sum_i C_i | i \rangle and the dual vector is defined as \langle \chi | =\sum_j D^*_j \langle j |Then, the an inner product is defined as \langle \chi | \phi \rangle =\sum_{ij} D^*_j C_i \langle j | i...
  44. D

    Particle Physics- Isospin states

    Hi, I have attached the question to this post. I understand on the process on getting to the answer in that you use $$\arrowvert 2, 2\rangle=\arrowvert 1,1\rangle \otimes \arrowvert 1,1\rangle$$ and apply the isospin-lowering operator to obtain $$\arrowvert 2,1 \rangle$$. Then I understand you...
  45. J

    I Accuracy of the Density of States

    I'm trying to understand the detailed concept of why the density of states formula is accurate enough to calculate the number of quantum states of an energy level, including degeneracy, within a small energy interval of ##dE##. The discrete energie levels are calculated by $$E = \frac{h^2 \cdot...
  46. L

    A Coherent states: Orthonormal set? Overcomplete basis?

    For two different coherent states \langle \alpha|\beta \rangle=e^{-\frac{|\alpha|^2+|\beta|^2}{2}}e^{\alpha^* \beta} In wikipedia is stated https://en.wikipedia.org/wiki/Coherent_state"Thus, if the oscillator is in the quantum state | α ⟩ {\displaystyle |\alpha \rangle } |\alpha \rangle it is...
  47. I

    (QM) Number of states with Energy less than E

    Hi, so I'm having trouble with a homework problem where it asks me to find the number of states with an energy less than some given E. From this, I was able to work out the energy E to be $$ E = \frac{\hbar^2}{2m} \frac{\pi^2}{a^2} \left( n_x^2 + n_y^2 + n_z^2 \right) $$ and...
  48. Zohar

    Oxidation States of Molecules and Atoms and the Relationship with Charges

    Hey, y'all. I know the oxidation state of a carbon in an ethene is -2 while carbon in Acetylene is -1. As well I know acetylene has more disspating elcetrons due to pai bonds. So how come charges between the acetylene carbon are more negative than in ethene while the carbones oxidations states...
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