State Definition and 1000 Threads

Homework Statement A damped harmonic oscillator is driven by an external force of the form $$F_{ext}=F_0sin(\omega t)$$ Show that the steady state solution is given by $$x(t)=A(\omega)sin(\omega t-\phi)$$ where $$ A(\omega)=\frac{F_0/m}{[(\omega_0^2-\omega^2)^2+4\gamma^2\omega^2]^{1/2}} $$ and...

For people who hit their head and suffer loss of mathematical and linguistic ability, does it also affect their emotional state? I met a woman who hit her head on table while falling down when she was 14 years old. Now she is 30+ years old. She said after the fall she can no longer comprehend...

How do I know if some given state is and eigenstate of some given operator?

Lets say a state is defined by the minimal amount of independent variables to completely describe a system. One would come up with the (q,p)-phase-space for a point mass and as another example the Hilbert-space for quantum-states. Consider the very simple case of a standing wave in string...

I was just reading the thread about the dead cat/live cat. Is the state of the cat dependent on the knowledge of the observer?

Hi there, I am reading something about quantum numbers, there the author introduce the quantum number by solving Schrodinger equation for Hydrogen atom. It gives me an example when the principal quantum number n=4, there are four different sub-level ##s, p, d, f##. It also depicts the sublevel...

Hello, I have a question about steady state error. how can we get to the C? I think it has to be Ea(G1+D)G2=C which gives(R-NH)(G1+D)G2 / (1+(G1+D)G2H)=C

If we consider a box( in our quantum world ) with three balls having total mass 'M= m1 + m2 +m3' . After changing their positions, now, calculating the mass will give another value which is not equal to 'M' but 'M*=m*1 +m*2 + m*3)', which implies our mass is not conserved. then how could energy...

consider an irreversible cycle. There will be no changes in the state variables (like U, S) of the system undergoing the cycle, but for the surroundings, there will be change in the state variables, in fact, entropy increases. my question is, what happens to the internal energy of the...

Homework Statement |1> and |2> form an orthonormal basis for a two-level system. The Hamiltonian of this system is given by: \hat{H} = \epsilon \begin{pmatrix} 1 & i \\ -i & 1 \end{pmatrix} a.) Is this Hamiltonian hermitian? What is the significance of a hermitian operator? b.) Find the...

Hello, I need to learn how Solid State NMR and X-ray Crystallography work (theory and practical application). I'm primary interested in how those experimental techniques are used to determine molecular structures. I'm an undergrad physics student and I need this to pass my final exam. So if some...

Hello! I am reading something about representation theory (just started) and I encountered this: "We will denote the state in the adjoint representation corresponding to an arbitrary generator ## X_a ## as |## X_a ##>". What is the state of a generator in a certain representation? Thank you!

Homework Statement Given a density matrix of three qubit pure state, how can I know after do some transformation, this state belong to what class?. Class I mean here, either separable state, biseparable, GHZ state or W state? I mean here what is the indicator to me classify it? It is the...

Homework Statement Q3a [/B] Copper (Cu) crystallises in a face-‐centre cubic (fcc) structure (with a basis of one copper atom). Draw a diagram of the unit cell of Cu, on your diagram indicate the (1, 1, 0) lattice plane and the [2, 2, 1] lattice direction. Q3b: Calculate the...

Homework Statement I am trying to calculate the wigner function for the even coherent state or cat state gives by, | \psi \rangle = N_+ \left( |\alpha \rangle + | -\alpha \rangle \right), where ##|\alpha \rangle ## is a coherent state and ## |N_+|^2 = \dfrac{1}{ 2 + 2e^{-2|\alpha|^2}}##. I am...

I’m confused about how you find the vector |s;s⟩ to use in the general equation |θ,ϕ⟩=exp(−iϕS3) * exp(−iθS2) |s;s⟩ For spin Coherent states (From http://www.scholarpedia.org/article/Coherent_state_(Quantum_mechanics)#4._Spin_Coherent_States Eq 12) Or how you find the vector |j,m=j⟩ to use...

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...

Hi all! I know that the singlet state is entangled. Is the center triplet state also entangled? At first blush it seems like it should be as the state expression has the same structure with the minus sign replaced by a plus. Thanks in advance!

Hi all My question: One of the four Bell's state are measuring in the Bell basis. Whether the result of measurement of this one of the four Bell's state will be the same Bell's state (just that Bell's state which are measuring) ? The each of four Bell's state is a quantum superposition of the...

[Sorry for the vague title, had a limit.] I have a question given in my Astronomy class: Below is a list of possible ways in which the universe could have been different. Some of these changes would make life as we know it impossible in our universe. Tick the boxes next to all the changes that...

3 forces, 5N,6N and 7N act on a particle which remains in a state of equilibrium. What is the angle between the 5N and 6N force?

How does one write a Lagrangian of a coherent state of vector fields (of differing energy levels) in terms of the the individual Lagrangians? I desperately need to know how to know to do this, for a theory of mine to make any progress. Please stick with me, if I didn't make sense just ask...

On the Schrodinger cat, can I simply say, outside the box,the state is in superposition,but inside the box, the state is not. Besides, the experiment is so simple to do, how come no body ever did it ?. Just put an animal you hate or even an inset, and observe the expected (50% -50%) result...

Does a 'weak measurement' on the spin of an electron in a pure state put the electron in a mixed state of the previous state and the state of the measurement axis of the measurement?

Hi folks, Let's pick a simple example, the H atom. We can calculate all spherical armonics, all quantum numbers so we are able to know which are all the possible states of the electron. We know all the values this observables can take. But the question is, let's say we have a handbook of...

I am trying to find the steady states in the ODE system. Assuming y0 = 2.5 * 10^5, I want to calculate y1, y2, y3 at the steady state. I do not understand how this would be possible, because only y0 is given and the following: d0 = 0.003, d1 = 0.008, d2 = 0.05, d3 = 1, ry = 0.008, ay = 1.6/100...

Hi, guys. If you are given one state of the baryon decuplet (the upper-right state ##\Deltaˆ{++}=uuu##, for instance), you can use the ladder operators to get the other states of the decuplet. When I apply ##T_-## to uuu and normalizing, I get ##\frac{1}{\sqrt{3}}(duu+udu+uud)##. However, in...

An allowed state of a molecule in a gas that is in a box of length L can be represented by a point in 3 dimensional K-space, and these points are uniformly distributed.In each direction points are separated by a distance π/L. A single point in K-space occupies a volume (π/L)^3. The number of...

I wasn't sure if I should post this in general discussion or in solid state section, but am I the only one who finds the Kittel textbook horrible? It seems full of semi-empirical, basic math, and boring, surface level observations written as dryly as possible. I really like solid state physics...

I have a question that seems to reflect my main concern with QM. Here it is: Consider a series of polarisation-entangled photon pairs that are sent in opposite direction to two measuring devices (e.g. at opposite ends of the universe). The measurement consists of detection of a photon after...

So I am so beyond stuck and my advisor told me that my progress is very slow. I made a post before about how I'm new to coding and everything, but now I kind of have to forget about the "learning" and make progress. Does anyone have tips on understanding the Baum-Welch algorithm...

Homework Statement A pore has three configurations with the energy levels shown. The pore is in thermal equilibrium with the surroundings at temperature T . Find the probabilities ##p_1##, ##p_2##, ##p_3## of being in each level. Each level has only one microstate associated with it. Also...

Hi folks, I know the work from Galois showing it is not possible to solve certain equations using only a certain type of numbers. But that was more than 100 years ago, I suppose lots of progress has been made on this topic. So my question is, What has been discovered to solve polynomial...

I just have a quick question about a concept I think I haven't fully grasped from my cosmology course. Why does non-relativistic energy have an equation of state with w=0? Also, is the concept of pressure different in general relativity than in thermodynamics or statistical mechanics?

Hi, I have been trying to get my head around the effect of a time reversed hamiltonian ##H^B(t)=H(-t)=T^{-1}H^F T ## on a state ket ##|\psi>##, where ##H^F=H## is the regular hamiltonian for the system (energy associated with forward time translation) and ##H^B=H(-t)## is the time reversed...

Homework Statement If the system is in a state |ψ> = 1/sqrt(6) |v1> + 1/sqrt(3) |v2> - i/sqrt(2) |v3> with Hamiltonian satisfying H|vj> = (2-j)a|vj> Find the mean value of energy <E> and the root mean square deviation √(<E2> - <E>2 ) that would result from making a number of measurements of...

Do all electrons orbit in the ground state, when the band gap, is increased, or decreased, as atoms come together to form molecules.? Like in glass, transparent liquids, and plastics. As atoms come together to form glass, like silicon, sodium, and calcium. Do the electrons orbital permanently...

Hi everybody. I was reading about the singlet and triplet states. It makes sense that we use an antisymmetric wavefunction for the singlet state, as we are talking about two fermions. But why are we using a symmetric wavefunction for the Sz = 0 triplet state? Doesn't this go against the...

I understand that if we have a quantum mechanical system, then its state at some given time ##t## is fully described by a state vector ##\lvert\psi(t)\rangle## in a corresponding Hilbert space. This state vector containing all possible information about the distributions (of all possible values)...

I have to filter data with Kalman filter. I know process error covariance Q and measurment error covariance R. Problem is with state transition matrix A, control matrix B and observation matrix H. First of all, data goes through this transfer function: ##W(s) = \frac{4s}{4s+1}## I can't get it...

I have found a couple other threads like this but I am looking for something at a very beginning level. I joined an experimental condensed matter group for the summer at the school where I will be matriculating as a first-year graduate student in the fall. They study various...

Homework Statement {Moderator edit: The unlabeled resistance is given to be 3.2 Ω } finding v1 and v2 at t=0+ and t=0- is needed Homework EquationsThe Attempt at a Solution ok I've found the currents by mesh analysis but how can i get the voltage?What voltage is in the inductor or capacitor...

I'm reading through my quantum physics lecture notes (see page 216 of the lecture notes for more details) and under the ladder operators section there is a discussion of the expectation value of ##L_x## for a state ##\psi = R(r) \left( \sqrt{ \frac{2}{3}} Y_{11} - \sqrt{ \frac{1}{3}} Y_{10}...

Homework Statement [/B] My question is more about the math of the problem. For equation 22.97, how do I construct a 3x3 matrix from a 12 element series? After constructing the matrix should I set the determinant equal to 0 where I will find the determinant has 3 solutions (2 being...

Hi all, I am reading some introducing materials on quantum information and quantum walk. In some materials, the author mentions to implement the related system with cold atoms and they mention the internal states. I learned the quantum mechanics some times ago but I didn't see any chapter in...

Consider addition of two angular momenta J = J1 + J2 , with j1=j2=1. Find the eigenstates of the total angular momentum I jm > in terms of the product states I j1 m1 j2 m2 > in two ways (a) Make use of the tables of the Clebech _Gordan coefficients (b) The state with m1 = m2 = 1 must be a...

I am working on a paper about Ammonia masers. It looks like Ammonia molecules are usually found in a superposition of even and odd parity states that are eigenstates of the inversion potential. That is the double well potential of the Nitrogen to tunnel through the Hydrogen plane. If it...

Consider a system of two identical spin-1 particles. Find the spin states for this system that are symmetric or antisymmetric with respect to exchange of the two particles. (Problem 13.3, QUANTUM MECHANICS, David H. McIntyre) I know that for bosons, the total wavefunction should be symmetric...

Homework Statement A gaussian wave packet is given by the formula: Ψ(x)=(1/(π1/4d1/2))eikx-(x2/2d2) Calculate the expectation value in this quantum state of the momentum squared. Homework Equations <p2>=-ħ∫Ψ*(X) (d2Ψ(x)/dx2) dx ∫e(-x2/d2) dx= d√π ∫xe(-x2/d2) dx =0 ∫x2e(-x2/d2) dx = (d3√π)/2...

I have been struggling to solve the following problem for days. I was given the state space model of a circuit and asked to determine the system elements. So basically, I think I have to find a suitable circuit which describes the state space equation. I am not really sure how to approach this...