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. C

    Find the equation of state of each gas

    The problem is from the book "The Principles of Thermodynamics" by ND Hari dass. It looks trivial problem, but I am not able to form logical arguements for going into next step. For example, It seems like first gas has equation of state ##PV =nRT## and second has ## \left( P_2 +\frac{a}{V_2^2}...
  2. Demystifier

    A States & Observables: Are They Really Different?

    Usually states and observables are treated as fundamentally different entities in quantum theory. But are they really different? A state can always be represented by a density "matrix", which is really a hermitian (or self-adjoint) operator. Since observables are also hermitian (or self-adjoint)...
  3. Sciencemaster

    I How can I model squeezed states in 3D optical modelling software?

    I would like to model squeezed light and its evolution (such as when passing through lenses after being generated) using optics software such as OptiFDTD or ZEMAX. However, I don’t see any way to make such states…my plan was to simulate an Optical Parametric Amplifier to generate these states...
  4. Halc

    I Do black holes destroy quantum states?

    This pop article popped up (isn't that what they do, by definition?) on my google news page. https://www.sciencenews.org/article/black-hole-paradoxes-quantum-states It claims that a thought experiment shows that doing a double-slit experiment near a black hole event horizon can reveal...
  5. R

    A Bound states of an electron trapped in a dipole field

    The problem of bound states of an electron trapped in a dipole field is being studied by Alhaidari and company. (See, for example, https://arxiv.org/ftp/arxiv/papers/0707/0707.3510.pdf). It is not clear to me why the point dipole approximation is used everywhere in such calculations. Can't an...
  6. C

    Is there a rule that states that I should not divide in this scenario?

    So basically this is how I solved this problem: 1. ##f(x)=\log _{2} x^2 - 1## 2. ##0=\log _{2} x^2 -1 ## 3. ##1= 2\times \log _{2} x## 4. ##\frac{1}{2}= \log _{2} x## 5. ##2^{\frac{1}{2}}=x=\sqrt{2}## So I wrote coordinates to be (##\sqrt{2}##, 0) But apparently, that is not the only solution...
  7. Mohammad-gl

    A Can I calculate partial density of states using tight binding?

    I am studying a 2D material using tight binding. I calculated density of states using this method. Can I also calculate partial density of states using tight binding?
  8. cwill53

    Basic Quantum Circuit: States of Individual Qubits

    I have done part A so far below, but I'm a bit behind on my reading, so I don't quite understand the action of the controlled-NOT gate on a single qubit. What I have so written so far for part B is: Let ##\mathcal{H}=(\mathbb{C}^2)^{\otimes 3}##. Let ##|\psi _{q_i}\rangle_k## , ##(i\in\left...
  9. Like Tony Stark

    Mixed states and total wave function for three-Fermion-systems

    I've already calculated the total spin of the system in the addition basis: ##\ket{1 \frac{3}{2} \frac{3}{2}}; \ket{1 \frac{3}{2} \frac{-3}{2}}; \ket{1 \frac{3}{2} \frac{1}{2}}; \ket{1 \frac{3}{2} \frac{-3}{2}}; \ket{0 \frac{1}{2} \frac{1}{2}}; \ket{0 \frac{1}{2} \frac{-1}{2}}; \ket{1...
  10. R

    Phonon Density of States (PDOS) at Gamma Point

    Hello everyone! I'm trying to replicate phonon density of states (PHDOS) diagrams for some solids using Quantum Espresso. The usual way I do it is the following one: scf calculation at minima (pw.x) Calculation of dynamical matrix in reciprocal space with nq=1 or 2 (ph.x) Calculation of...
  11. Addez123

    Solving the Density of States: Understanding dn/dE

    $$n = \sqrt{n_x^2 + n_y^2 +n_z^2}$$ $$E = \frac{n^2 \pi^2 \hbar^2}{2mL^2}$$ $$n = \sqrt{ \frac{2mL^2E}{\pi^2 \hbar^2} }$$ This is all given by the textbook. It's even as friendly as to say $$\text{differential number of states in dE} = \frac{1}{8}4 \pi n^2 dn$$ $$D(E) = \frac{...
  12. M

    I States of equal energy are equally probable

    I'm reading "Statistical Mechanics: A Set of Lectures" by Feynman. On page 1 it says that, for a system in thermal equilibrium, the probabilities of being in two states of the same energy are equal. I'm wondering if this is an empirical observation or if it can be derived from QM?
  13. graviton_10

    Expected value of variance of Hamiltonian in coherent states

    I am trying to find the expected value of the variance of energy in coherent states. But since the lowering and raising operators are non-hermitian and non-commutative, I am not sure if I am doing it right. I'm pretty sure my <H>2 calculation is right, but I'm not sure about <H2> calculation...
  14. uxioq99

    Do Coherent States Imply 0 Energy Uncertainty?

    By considering the power series for ##e^x##, I assert that ##N=e^{-\lambda^2/2}## and that ##a\Psi_\lambda = \lambda \Psi_\lambda##. Because the Hamiltonian may be written ##\hbar \omega(a^\dagger a + 1/2)##, ##\langle E \rangle = \hbar \omega(\langle a \Psi_\lambda, a \Psi_\lambda \rangle +...
  15. yucheng

    I Fermi's golden rule: why delta function instead of density states?

    Sakurai, in ##\S## 5.7.3 Constant Perturbation mentions that the transition rate can be written in both ways: $$w_{i \to [n]} = \frac{2 \pi}{\hbar} |V_{ni}|^2 \rho(E_n)$$ and $$w_{i \to n} = \frac{2 \pi}{\hbar} |V_{ni}|^2 \delta(E_n - E_i)$$ where it must be understood that this expression is...
  16. Yuras

    B Spectral lines and superposition of states

    Let's say atom has two energy levels, ##E_1## and ##E_2##. If atom is in the first state ##|E_1\rangle##, then it's able to absorb a photon with energy ##E_2-E_1##, while transitioning to the second state ##|E_2\rangle##. In atom's spectrum we can see an absorption line at the corresponding...
  17. James1238765

    I Use of Gell-Mann matrices as the SU(3) basis for gluon states?

    The 8 gluon fields of SU(3) can be represented (generated) by the 8 Gel-Mann matrices: $$ \lambda_1 = \begin{bmatrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix} , \lambda_2 = \begin{bmatrix} 0 & -i & 0 \\ i & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix} , \lambda_3 = \begin{bmatrix} 1 & 0 & 0 \\ 0...
  18. LittleSchwinger

    I Single Photon States: Definition & Real-Life Applications

    A photon in QFT is defined in the same way as all particles. That is they denote a set of quantum states that transform in the simplest possible way under Poincaré transformations. Properly this is known as an irreducible representation (irrep) of the Poincaré group. You can classify these...
  19. H

    Stationary states infinite cubic well

    For a state to be stationary it must be time independent. Naively, I tried to find the values of c where I don't have any time dependency. ##e^{c \cdot L_z} \psi (r,t) = e^{c L_z} \sqrt{\frac{8}{l^3}} sin(\frac{2 \pi x}{l}) sin(\frac{2 \pi u}{l}) sin(\frac{2 \pi z}{l}) e^{-iEt/\hbar}##...
  20. Marioweee

    QFT: Normalization of coherent states

    What I have done is the following: \begin{equation} \braket{\eta_k | \eta_k}=|N|^2\sum_{n=0}^{\infty}\dfrac{1}{n!}\bra{0}(A^{\dagger})^nA^n\ket{0}=|N|^2\sum_{n=0}^{\infty}\dfrac{1}{n!}\int...
  21. gentzen

    I Are there asymptotic QTF/QED states in a constant magnetic field?

    It is "easy" to produce experimental setups that could and should for all practical purposes be described as having a constant background magnetic field everywhere, especially in the "asymptotic region" where the detectors are located. You can do this both in vacuum, and inside a solid sample...
  22. Ahmed1029

    I Can I find a particle in two states simultaneously?

    If I want to get the spin angular momentum of a particle using the Stem-Gerlach experiment, I think I will find the spin 1/2 particle either spin up or spin down, but not both. I however want to ask this : Is there a non-zero probability that a particle which is spin-up in the z direction to be...
  23. P

    I What are the possible states of cold iron balls?

    This thread is meant to discuss a topic that arose in https://www.physicsforums.com/threads/is-there-a-theoretical-size-limit-of-a-planet.1045983/ in a more precisely specified, idealized way. Further details: 1) Standard model + GR assumed, no other theories intended for this...
  24. B

    A Dressed states for a 3 level system

    Hello! If we have a 2 level system (I will call the states g and e for ground and excited), and a laser field (which can have any detuning relative to the spacing between g and e), it can be shown that that the total number of particles is conserved under the laser-atom interaction hamiltonian...
  25. S

    Spin-1 particle states as seen by different observers: Wigner rotation

    Summary: Suppose that observer ##\mathcal{O}## sees a ##W## boson (spin-1 and ##m > 0##) with momentum ##\boldsymbol{p}## in the ##y##-direction and spin ##z##-component ##\sigma##. A second observer ##\mathcal{O'}## moves relative to the first with velocity ##\boldsymbol{v}## in the...
  26. Dario56

    I Density Operators of Pure States

    Quantum states are most often described by the wavefunction ,##\Psi##. Variable ,##\Psi(x_1x_2\dots x_n) \Psi^*(x_1x_2\dots x_n)## defines probability density function of the system. Quantum states can also be described by the density matrices (operators). For a pure state, density matrix is...
  27. Astronuc

    History History of the United States, Vol I, Charles and Mary Beard, 1921

    I just happened to hear this one night last week. It is a history of the US from the perspective of two historians from the early 20th century. https://librivox.org/history-of-the-united-states-vol-i-by-charles-and-mary-beard/ https://librivox.org/group/495 I was listening to this around the...
  28. robphippen

    I Understanding Spin States in 2D Vector Spaces

    There is a passage in this book where I don't follow the logic; In this short quotation from 'Quantum Mechanics: The Theoretical Minimum' by Leonard Susskind and Art Friedman \mathcal{A} represents the apparatus that is performing the measurement the apparatus can be oriented (in principle) in...
  29. Simobartz

    I Bragg condition and Bloch states

    I'm reading about Bloch states, these the are states of electrons in a periodic potential. What i know is that the electron in a Bloch state is shared between many ions and it is a stationary state. However, for a 1-dimensional model I've read that at the edge of the first Brillouin zone, when...
  30. patric44

    Calculate the isotopic shift of the analogue states for Cr and Mn

    hi guys my nuclear physics professor gave us a hand written notes about a the isospin multiplets of elements, the notes provides a brief not clear introduction to the topic with some formulas for calculations, as following $$ E_{xe} = \Delta\;E_{B}+\Delta\;E_{c} $$ $$ \Delta\;E_{B}=...
  31. Jamister

    A Measurement of the phase of coherent states

    It is commonly said that the phase of coherent states can't be measured, just the relative phase between two coherent states. A qubit example: define the states $$|\phi\rangle=[|0\rangle+\exp (\mathrm{i} \phi)|1\rangle] / \sqrt{2}$$ and the measurement operators...
  32. C

    Are the states (or set of states) absorbing, transient or recurrent?

    Summary: Determine the absorbing states & communication classes of the given matrix. Hello everyone, If we have a state space of S = {1,2,3,4} and the following matrix: \begin{bmatrix} 0 & 1 & 0 & 0\\ 0 & 0 & 1/3 & 2/3\\ 1 & 0 & 0 & 0\\ 0 & 1/2 & 1/2 & 0\\ \end{bmatrix} Now, given the...
  33. Salmone

    I Linear combination of states with Pauli's principle

    If I have two identical particles of ##1/2## spin, for Pauli's exclusion principle all physical states must be antysimmetrical under the exchange of the two particles, so ##\hat{\Pi}|\alpha\rangle=-|\alpha\rangle##. Now, let's say for example this state ##\alpha## is an Hamiltonian eigenfunction...
  34. sliqu

    I Vanadium oxide oxidation states binding energy -- unequal spacing

    Hello, How come in XPS the binding energy gaps between oxidation states of vanadium oxide are not equally spaced? Is there a reason they are not all equally spaced? V2+ (VO) 513.0 eV V3+ (V2O3) 515.6 eV V4+ (VO2) 516.0 eV V5+ (V2O5) 517.1 eV Many thanks
  35. this_is_my_name

    Calculate qubit states with Schrodinger's equation

    Summary:: How to calculate qubit states with the Schrodinger eq I'm writing something about the relation between quantum computers and the Schrodinger equation. One of the requirements is there has to be an experiment. So I thought I could measure some qubits that have results and then do the...
  36. S

    How to describe and discuss different solid matter states?

    The possible forms of solids can be more than just amorphous solids and crystalline solids. I tried a look at a couple of wikipedia articles and one of them showed descriptions of Plasticity, elastic, and Viscoelasticity, but those are not enough. I can only think to give some real world...
  37. guyvsdcsniper

    States in the Hydrogen Atom that are not allowed

    I am a little lost on how to approach this problem. What I know is the following: The r vector is in terms of x y and z hat. I know my two l=0 states can be the 1s and 2s normalized wave function for Hydrogen. Should I be integrating over dxdydz?
  38. Mr_Allod

    Edge States in Integer Quantum Hall Effect (IQHE)

    Hello there, I am having trouble understanding what parts b-d of the question are asking. By solving the Schrodinger equation I got the following for the Landau Level energies: $$E_{n,k} = \hbar \omega_H(n+\frac 12)+\frac {\hbar^2k^2}{2m}\frac{\omega^2}{\omega_H^2}$$ Where ##\omega_H =...
  39. ergospherical

    I Effective mass in terms of electron states

    I'm trying to figure out the second order extension of the "trick" used on page 92 (https://www.damtp.cam.ac.uk/user/tong/aqm/solid3.pdf) for the calculation of the effective mass matrix ##m^{\star}_{ij} = \hbar^2 (\partial^2 E/ \partial k_i \partial k_j)^{-1}## on page 94. I think for this one...
  40. Neo Tran

    The occupation probabilities of electrons in different states

    occup is proportional to [gi x exp(-Ei/kT)] where gi is the numver of states at energy Ei
  41. D

    A "Cross-section" and "half-life" of excited states

    Hello, I work with a spectrometer that does ionizations through laser 2+1 photons resonant ionization (a high power narrow bandwidth laser is tuned to a precise wavelenght so that it allows reaching an excited energy level of a particular element with the sum of two photons absorbed...
  42. P

    Engineering Why Are Some System States Indistinguishable in Observability Analysis?

    https://en.wikipedia.org/wiki/Observability I am studying observability and I try to get some intuition on the topic. Given the observable matrix, we can find the null space. However, the vectors of the null space are states but this differs from the definition of what a state vector of a...
  43. F

    A Majorana representation of higher spin states

    In the article by E. Majorana "Oriented atoms in a variable magnetic field", in particular, it's considered (and solved) the problem of describing a state with spin J using 2J points on the Bloch sphere. That is, if the general state of the spin system , (1) then, according...
  44. benagastov

    Finding all possible energy states faster without using a calculator

    I tried to find states in direct method using ##\frac{E}{E_0}=\:nx^2+ny^2+nz^2## and ##100\:<nx^2+ny^2+nz^2\:<\:136## But it was too long, found it using phi approximation there are around 300 energy states, and Python find around 271 states using direct method but I need manual or recursive...
  45. einheit

    I Are all (pure) states physically realizable?

    To elaborate that summary a bit, suppose ##\mathcal H## is the Hilbert space of the particle, with ##\mathcal{H}_2\subseteq\mathcal{H}## its two-dimensional spin subspace. Now consider any ##|x\rangle\in\mathcal{H}## such that ##|x\rangle\perp\mathcal{H}_2##, i.e., ##\forall ~...
  46. Twigg

    I Does putting a hydrogen atom in a box mix angular momentum states?

    If you put a hydrogen atom in a box (##\psi=0## on the walls of the box), spherical symmetry will be broken so ##n##,##l##,##m_l## are no longer guaranteed to be good quantum numbers. In general, the new solutions will be a linear combination of all the ##|n,l,m_l\rangle## states. I know that...
  47. K

    A Mixed versus Pure Quantum States for the Singlet

    I have some basic questions about mixed states and entanglement. 1. Do mixed states always imply that the states are entangled and vice versa? 2. Can mixed states ever be separable? 3. Does interference have anything to do with entanglement? In terms of Density Matrices, ρ = |ψ><ψ|: 4...
  48. S

    When it states "in terms of a, b, c" do you need to use all variables?

    This is a spring problem From this, it says I need to answer in terms of kinematic friction which to me doesn't make much sense. I also looked at similar questions online to the "in terms of" problems and they don't use all four variables in their derived equation. Do I not need to use all...
  49. Rikrik

    B Boundary between a particle in two energy states

    Hi I'm new to quantum mechanics, Looking for some help regarding a concept i am struggling to solve. I am curious if I had a cube of particles in a ground state and another cube with the same particle in a higher energy state. If I placed one upon another, is there anything in quantum mechanics...
  50. chikchok

    Phonon density of states and density of states of free electrons

    In the following pdf I tried to calculate the density of states of free electrons and phonons. First, I found the free electron DOS in 1D, it turns to be proportional to (energy)^(-1/2) and in 2D it is constant. However, I am not sure I found the DOS for phonons in the second part of the...