States Definition and 1000 Threads

Homework Statement I'm dealing with a dirac particle in an attractive spherical square well. I've solved for the transcendental equation to find energy, found the normalized wave function, and now I'm trying to explain what happens when the well becomes very deep, when V0 ≥ 2mc2. If I plug...

Hi all, what is the meaning/difference between perturbative and non perturbative vaccum.

For spin-1/2, the eigenvalues of S_x, S_y and S_z are always \pm \frac{\hbar}{2} for spin-up and spin-down, correct? What is the difference between eigenvectors, eigenstates and eigenspinors? I believe eigenstates = eigenspinors and eigenvectors are something else? I'm just getting confused...

"Neutrons don't decay in nuclei because no available states" incorrect? Hello, If I understand correctly, the argument for a neutron (usually) not decaying when in a nucleus, is that the resulting proton would then have to occupy a high energy level, the lower levels already being occupied...

My book calculates the ratio of probability to find an atom in an excited state vs finding it in the ground state in the sun and gets approx 1/109. Essentially this must mean that the ratio of the multiplicities of the system must also be equal to this, i.e.: \Omega2/\Omega1 = 1/109 How...

this reminds me of a question that I'd like to ask. as a chemist, my view of quantum mechanics is that it is a useful tool to give the right answer for spectroscopy calculations and to make a model of complicated molecules so that we can pin down some parameters with instruments, then get the...

How do we know when we can write a product state for two systems, and situations when you need to use a sum of product states? If you have a product state for two systems, does it evolve into a sum?

I'm trying to follow Feynman's explanation on page 9-3 of Volume 3 of The Feynman Lectures on Physics. I've attached a copy of the section in question. To normalize CII he notes that < II | II > = < II | 1 >< 1 | II > + < II | 2 >< 2 | II > = 1 I am not clear how he derives the conclusion...

\begin{align} \dot{x} =& -x + ay + x^2y\notag\\ \dot{y} =& b - ay - x^2y\notag \end{align} The only steady states are $(-b,0)$ and $\left(0,\frac{b}{2a}\right)$, correct? I feel like there should be more but I don't think there any.

Hi everybody! I'm studying this paper "Unambiguous discrimination among quantum operations" http://pra.aps.org/abstract/PRA/v73/i4/e042301 and they state that Ok, it's well known, but then I took a review of the notes to my course of quantum information and i found this not proven proposition...

$N_{t + 1} =\begin{cases}rN_t^{1 - b}, & N_t > K\\ rN_t, & N_t < K \end{cases}$The steady states are when $N_{t + 1} = N_t = N_*$. $$ N_{*} =\begin{cases}rN_*^{1 - b}, & N_* > K\\ rN_*, & N_* < K \end{cases} $$ So the steady states are $N_* = \sqrt[b]{r}$ and $N_* = 0$. I am not sure how to...

I'm simulating an ion beam with different charge states passing through two pinholes. I'm using random angles, from an external function, to evaluate the velocity components along the axes and solving the differential equation: O=[0 0 0]'; f = @(t,ys) [ys(4:6); O]...

So the book is showing an example about discrete steady states but neglected to show how the steady states were found. Here is what it has $u_{t+1}=ru_{t}(1-u_t), \quad r>0$ where we assume $0<r<1$ and we are interested in solutions $u_t>0$ Then it list the steady states $u^*=0, \quad...

US states using the concept of IDR?? While I'm reading IAEA safety report 47, I've learned the concept of IDR, instantneous dose rate, which is commonly used in UK. IDR is the tool for recommendation of the limit of high dose rate in a short time, e.g., an hour. Generally, in US, NCRP is the...

Hello, everyone: My question is about the states of paired electrons in BCS Theory. According to Tinkham's book (pages 70-71), electron states in the superconducting gap (SG) in normal state are push up to above the upper edge of the SG in superconducting state; on the other hand, it seems...

I am trying to show that there are 3 nonzero steady states of \frac{du}{dt}=ru\left(1-\frac{u}{q}\right)-\left(1-\exp\left(-\frac{u^2}{\varepsilon}\right)\right)=0 I have tried using Mathematica and Mathematica couldn't solve it. I tried some algebra and that wasn't going anywhere so I am at a...

Homework Statement What is the uncertainty in x and p of the coherent state |z> = e^{-|z|^2/2} \sum\frac{z^{n}}{\sqrt{n!}} |n> Homework Equations ... The Attempt at a Solution This seems pretty straight-forward to me. You just find the expected value of (let's say) x...

Steady states for a system of nondimensionalized DEs $$ \begin{array}{lcl} \frac{du_1}{d\tau} & = & u_1(1 - u_1 - a_{12}u_2)\\ \frac{du_2}{d\tau} & = & \rho u_2(a - a_{21}u_1) \end{array} $$ So $(0,0)$ and $(1,0)$. Are there any more? If so, how did you find them?

I need to demonstrate that there are 3 possible nonzero steady states if r and q lie in a domain in r,q space given approximately by rq>4. Could this model exhibit hysteresis? The below ODE is nondimensionalized. $0<\varepsilon\ll 1$ $\displaystyle \frac{du}{d\tau} = ru\left(1 -...

Hi, I was wondering if people could share with me their experiences of the workload associated with postdoc positions in the states. I am thinking of applying for some positions but i am put off by what i have previously heard - that as a postdoc you can end up doing the majority of the work...

Homework Statement I need to investigate Glauber Coherent States and I have no clue where to begin. I need to define a superposition of two coherent states with amplitudes 2.6 and -2.6 in a potential with V0=0.65 Homework Equations Schrodinger Eqn. E ψ(x) = -1/2 d^2/dx^2 ψ(x) + V0...

I have been doing some reading into Glauber Coherent States and I am struggling to get a grasp on how they are composed, ie. how to determine when they exist. I kind of get the idea (qualitatively speaking) let me try to explain what I think; - They are composed of superpositions of many of...

It doesn't seem like a time dependent hamiltonian would have stationary states, am I wrong? I've run into conflicting information.

The only ones I can think of are bose-einstein condensate in the same realm as super-liquids/solids, solid, solid-liquid, liquid, liquid-gas, gas, plasma, quark/gluon plasma, metallic or degenerate hydrogen (I guess critical point?), and degenerate neutronium and whatever singularities are made...

QM says that states which are simultaneous eigenstates of two commuting observables are allowed. If you don't have such states to start with you can construct them with the Gramm-Schmidt orthogonalization procedure. Consider the excited states of a nucleus. (They can be considered eigenstates...

The following lecture from University of Oxford contains an explanation of the constancy of probability distributions for all observables when a system is in a stationary state: http://www.youtube.com/watch?v=0yvX4jhzblY#t=15m35s. However, the derivation of the vanishing amplitude does not...

Following Griffiths derivation on pg 44 of the eigen-states of SHO Hamiltonian, he says that we can now find all eigenvalues, but doesn't say how he knows that a and a dagger will indeed take you between nearest neighboring orthogonal states. in other words, how do we know the ladder...

Density of States Derivation -urgent Homework Statement Homework Equations λ=h/Px (Px = x momentum) L/λ=nx The Attempt at a Solution A summarized derivation from the lecturer has proven to be problematic when revising: as same in xyz direction just cube one direction...

Homework Statement an operator for a system is given by \hat{H}_0 = \frac{\hbar \omega}{2}\left[\left|1\right\rangle\left\langle1\right| - \left|0\right\rangle\left\langle0\right|\right] find the eigenvalues and eigenstates Homework Equations The Attempt at a Solution so i...

Homework Statement Demonstrate the relation between the expectation value and the measurement outcomes of an observable of a particle by conisdering as an observable the kinetic energy operator E=p^/2m when the particle is in a superposition of 2 momentum eigenstates Homework Equations...

I know its number of states per unit energy but what happens in the case of continuous energy?

Homework Statement There are two independent subsystems with angular momenta j1 = j2 = 1. States have to be found for the whole system with angular momentum j = 2. Homework Equations Basic procedure for addition of Angular Momentum in Quantum Mechanics The Attempt at a Solution Basically j...

See Attachment for Question See Attachment for Answer from back of book I do not see how part a and part b are asking me two different things. I interpret the first part of part a "Is b in {a_1,a_2,a_3}?" as Is b a solution of the system represented by matrix A? [1,0,-4,4 0,3,-2,1...

The law of inertia states roughly that an object will remain in it's current state of rest or motion unless acted upon by an external force. So if for example I wanted to move a ball of mass m from stationary I would have to overcome the inertia. Ok so if I wanted the ball to accelerate at...

Homework Statement See attachment Homework Equations The Attempt at a Solution I'm not sure how to determine which points are co linear or which point lies in between the two. My book doesn't discuss how to do this at all. but PQ→ = <1,-1,2>, PR→ = <3,-3,6> I believe I found...

Homework Statement Consider an electron gas with a density of states given by D(e) = ae2. Here a is a constant. The Fermi energy is eF. a) We first consider the system at zero temperature. Compute the total number of electrons N and the groundstate energy E. Show that the average energy per...

In the symmetrical potentials the Eigenstates are either even or odd. why the even states have less energy than odd states?

Hi all, My Physics tutor's reasoning for no well-defined energies existing in nature for a system in time was that if a system had a well defined energy in time, such that |psi> = |E0> then, evidently, the energy cannot vary. And, his logic goes on to say that if an energy cannot vary, you...

Homework Statement The number of electron states in a subshell with orbital quantum number l = 3 is: A. 7 B. 9 C. 14 <-- answer D. 2 E. 3 I am reviewing for a comprehensive final and maybe its all the studying but I am lost here.. Homework Equations n=/=0 l= 0--> (n-1) m =...

Homework Statement See Attachment Calculate the force of gravity on the point mass due to the line mass in terms of the gravitational constant G, m, M, D, and L. The line mass has a uniform density. Homework Equations The Attempt at a Solution Ok so apparently I'm suppose to...

Homework Statement See attachment. In the system shown below, the spring is initially at its equilibrium length, L, and the block has a velocity down the ramp of 5 m/s. At the point where the block stops and turns around, the spring has a length of L + ΔL. Calculate ΔL. The ramp is...

I understand that it is important for two eigenvectors to be orthogonal, but what is it exactly about mutually exclusive states that makes them orthogonal?

I know that UV-Vis spectroscopy is based on the principle of electrons jumping to higher energy states but I just read that each energy state has a number of "vibrational energy levels" inside it. Heres a diagram: I'm confused now, what is a vibrational energy level and what is an energy...

Homework Statement Find the slope of the line tangent to the polar curve at the given point. At the point where the curve intersects the origin, find the equation of the tangent line in polar coordinates. r = 6 sinθ; (-3 7∏/6) Homework Equations The Attempt at a Solution...

I'm a bit unclear on exactly what a coupled state really means and how to represent it, so here's what I have: Homework Statement Consider the coupling of two spinless l=1 particles, What possible product states |1\, m_1 \rangle \otimes |1\, m_2 \rangle are there and what possible coupled...

Article: "Faked States" mimic quantum entanglement Does anyone know where to find a copy of this that isn't pay-walled? http://physicstoday.org/resource/1/phtoad/v64/i12/p20_s1?isAuthorized=no

Hey, I'm learning about quantum computing for a project and I'm a bit stumped about a concept: They say in quantum computing you can have the superpostion of all possible states, then perform an operation on that wavefunction, and thus have all possible states processed in one operation...

I am new to quantum physics. My question is how to write the Hamiltonian in dirac notation for 3 different states say a , b , c having same energy. I started with Eigenvaluee problem H|Psi> = E|psi> H = ? for state a? SO it means that indvdually H= E (|a><a|) for state a and for all three...

The experimental team takes a sample of the population to probe. I know QM can predict an expectation value for observable A. When the results are returned, there is an experimental value +/- uncertainty. For a verification, would the result need to concide with the expectation value? Would...

In atom spectrum, such as for hydrogen, there are states of 1s, 2s, 2p, 3s, 3p, 3d, etc. There are no 1p, 1d or 2d, 2f. Simply because n= n_r + L +1. So the maximum of L is n-1. But when I read articles talk about meson, they list meson states of 1p, 1d, 1f, etc. Such as in the article “Quark...