Ground state Definition and 275 Threads

ground states Homework Statement Is it generally true that the ground state of a given quantum system corresponds to the lowest quantum numbers? For instance, is it generally true that the ground state of a system governed by a radial potential always corresponds to l=0? If not, how do we...

Homework Statement How many unpaired electrons are present in each of these species and what is the ground state? Given:1s2 2s2 3p1 Homework Equations none The Attempt at a Solution what is the ground state? I can find the number of unpaired electrons.

XXZ model in 1-dimension, with external field, what is the exact form of its ground state wave function? Recently I've read the ground state wave function of XY model and was curious about the condition of XXZ. Do they have a similar manner? The XY result is attached below. Thanks.

Homework Statement V(x) = k|x|, x \in [-a,a], V(x) = \infty, x \notin [-a,a]. Evaluate the ground state energy using the variational method. Homework Equations a = \infty and \psi = \frac{A}{x^{2}+c^{2}}. The Attempt at a Solution 1 =...

Is the ground state of the infinite square well an eigenfunction of momentum?? If so, why. If not, why not??

I am looking at a diatomic molecule where the Hamiltonian is given as H = l²/2I + F*d*cos theta where d is the dipole moment. The term F*d*cos theta is small. I write the energy of ground state as E_0 = \hbar*l*(l+1)/ 2I Than I have to determine how much the ground-state energy...

I'm working all alone with nobody to help me, and now I'm stuck! :( I'd really appreciate it if you could help me out. I'm working with the ground state of the one electron hydrogen atom. Trying to determine the radial dependence on probability density. It should only depend on the radial...

Hello. I'm trying to grasp this concept. The question states: An excited atom decays to its ground state and emits a photon of green light. If instead the atom decays to an intermediate state, what color of light might be emitted? I have the electromagnetic spectrum with the visible lights...

A particle in a potnetial V(x) has a definite energy E = - \frac{\hbar^2 \alpha^2}{2m} and its eigenfunction is given by \psi(x) = Nx \exp(-alpha x) if 0 <= x < infinity zero elsewhere Prove that V(x) = -alpha \hbar^2/mx 0 <= x < infinity infinity elsewhere Given that the...

I've been told (in class, online) that the ground state of the 3D quantum harmonic oscillator, ie: \hat H = -\frac{\hbar^2}{2m} \nabla^2 + \frac{1}{2} m \omega^2 r^2 is the state you get by separating variables and picking the ground state in each coordinate, ie: \psi(x,y,z) = A...

H=\frac{p^2}{2m'}+V_0(r)+V(r) where V(r)=2[3\frac{(S \cdot r)^2}{r^2}-S^2] and V_0(r) is a rotationally invariant potential, p=p1-p2, the relative momentum and m' the reduced mass. S=S1+S2 spin operator. Assume first that V(r) is zero; what is the degeneracy of the ground state...

Can someone explain to me why the ground state energy of a free electron fermi gas is not just: E = 2 \int_0^{k_f} \frac{\hbar^2 k^2}{2m} 3k^2 dk Where the factor of two is due to the fact that there are two electron states for each value of k. The idea is to add up all the energies of...

This is my second post concerning a question I had from Hawking book. I am completely new to this subject, and lack the mathematical background necessary to fully understand these concepts, but I hope that by posting my question I will at least not be so confused about it after receiving some...

hi can anyone please help me I came across this statement "Since we only consider the electronic ground state of the system, there can be no net force or torque acting upon the subsystem of classically behaving nuclei". Can anyone explain what this means?

What is the ground state energy of the following. (a) an electron Well the formula is: E_n = (h^2/(8*m*L^2))*n^2; The ground state means, n = 1, its the lowest enegery level possible. So i plugged in n = 1, mass of e = 9.11E-31; h = 4.136E-15 eVs; L = 100 pm, because the book says that's...

A particle has mass 'm' and potential V(x) = x^2. Find the ground state of this wavefunction. Should I use the Hamiltonian operator here?

If we calculate the ground state energy of a system we receive E=w*h(bar). This Energy can be derived with the harmonic oscillator. Is this Energy the Energy of a free photon or a free electron in (for ecample) the vacuum state or is this describing a particle between (potential,...) walls...

When doing L-S coupling scheme for (3d)4, I am asked to find the ground state. I know that the first step, according to Hund's rules, is to find the the S with the largest value (S, L are total values, s, l are individual values). It is obviously S=2. Next, I should proceed to find the largest...

anyone happen to know how to estimate the ground state energy of a vee-box using the uncertainty principle?

What is the most probable value of r for the grounds tate of hydrogen, and why? Is it just the Bohr radius?

I have some problems with the following question: Deduce what terms may arise from the ground state configurations of the atoms of elements of Period 2 and suggest the order of their energies using Hund´s rules. Deduce what terms may arise... Do they mean to which terms the atoms can be...

Does Light have a "Ground State"? Light when it gains or loses energy, increases or decreases its oscillation rate, and shortens or lengthens its wave length (respectively). Do anyone find it hard to imagine just how fast and short light was circa big bang? Is it possible, given enough time...

Using the ground state of the hydrogen atom Psi 1,0,0 = sqrt([pi]*a3) * e-r/a I get <r> the expected radius as <r> = 3a/2 where a = Bohr radius. Anybody happen to know if this correct? It would have been cooler if the Bohr radius in physical constants were <r> and the scale factor...

Ok, I am currently taking chemistry, and the course involves some aspects of quantum physiscs, such as bohr models, quarks, and orbitals. My teacher taught us that when the elcetrons become excited they move up an energy level. However they do not move in the traditional sense, "they are...

Hi, Why is that, the ground state eigenfunction in ANY quantum mechanical system is symmetric under inversion of co-ordinates?