Ground state Definition and 259 Threads

Homework Statement when using E=(h(pi)n)^2/(2mL) h=h bar m= mass of particle L= length this may be a dumb question but is the ground state 0 or 1 for n n=0,1,2...

Homework Statement Two neutral spinless particles of mass m are gravitationally bound to one another. What is the ground state energy of this two-particle gravitational atom? Homework Equations The Attempt at a Solution So, it's a two particle system, but H_{total} = H_1 +...

Hi, i worked through several examples where the ground state energy of a particle in an arbitrary potential V(r) is estimated with Heisenberg's uncertainty relation. In these examples they prepare the Hamiltonian for the particle. For example the Hamiltonian for a particle in a harmonic...

Homework Statement Calculate ground state of erbium [Xe] 4f^12 6s^2 The Attempt at a Solution so i know that the f orbital can hold 14 electrons and has 7 types of orbitals that is -3,-2,-1,0,1,2,3 So i constructed a table with axes of m_l (-3 to +3 above) and m_s. Then hunds rules...

if the ground state is non-degenearate, this is easily understood But what if the ground state is non-degenerate?

If you make the length of a finite well shorter, then the energy levels should increase, because for example the uncertainty principle. But can the ground state, when squeezed, have such high energy that the energy is greater than the potential of the well? Does that even make sense?

1. In a certain gamma decay process, an excited neon atom emits a gamma-ray that has an energy of 1.630 MeV. The neon atom in the ground state has a mass of 19.992 435 u. What is the mass of the excited neon atom? 2. I am pretty lost here. There must be a formula relating these...

Homework Statement What is the calculated binding energy of the electron in the ground state of (a) deuterium, (b) He^{+} and (c) Be^{+++}? Homework Equations For the hydrogen atom, E_{n} = - E_{o} / n^{2} E_{o} = me^{4} / 2hbar^2(4\piEo)^2 The Attempt at a Solution Not sure...

Homework Statement Hi all - I've done all but the last part of this problem, for which I have the solution, but I was hoping someone could explain why the solution is what it is :) q:The Hamiltonian of a quantum system suddenly changes by a finite amount. Show that the wavefunction must...

i am now reading some materials on lanczos algorithm, one of the ten most important numerical algorithms in the 20th century my puzzle is, why it is useful for finding out the ground state energy? i can not see anything special about the ground state energy in the algorithm

microwave can be used to engineering potentials for alkali atoms i find that in the literature, people only take the magnetic dipole transition into account why the electric dipole transition is neglected? is it forbidden?

Just a short question. I have five energies. -25 eV -5 eV 0 eV 5 eV 25 eV The textbook definition is that the ground state is the state with the lowest energy, i.e. I believe 0 in this case. But that is taking the absolute value of theenergies. In reality the lowest energy is...

Hello, Non-relativistic quantum mechanics doesn't explain why the electron in the hydrogen atom (for example) "decays" from excited states to the ground state. Which theory does explain this phenomenon (from basic principles) ? Thanks.

Homework Statement The particle in a box model is often used to make rough estimates of ground state energies. Suppose that you have a neutron confined to a one-dimensional box of length equal say 1 x 10^-14m. What is the ground state energy of the confined neutron? answer in MeV...

Homework Statement an electron moves in 1D and is confined to the right half (x>0) potential: V(x) = -(e^2)/(8piEx) E is the permittivity of free space the ground state wave function is Nxe^(-ax) N is normalization constant, and a is another constant needed to be determined Homework...

Is the ground state of any negative potential that goes to zero at + or - infinity always even?

Homework Statement using first-order perturbation theory ,estimate the correction to the ground state energy of a hydrogenic atom due to the finite size of the nucleus, assume it's spherical nucleus. Homework Equations you can employ the fact that the electrostatic potential fi...

How many magnetic flux quanta exist within the ground state hydrogen atom? Thanks in advance.

Hi all: As we know, if we solve the schrodinger equation, the ground state wavefunction is independent of theta and psi. We find the expectation value of ground state orbital angular momentum is zero. But if we don't do any mathematical calculation, can we conlude that? For example, Due to...

In QM, sometimes we will combine the delta potential and other familiar potential (like infinite potential well). And I am quite confuse with the bound state. For example, consider a 1D infinite potential well with width a and locate b/w [-a/2, a/2]. Now if we add in a delta potential...

If I know the explicit form of potential, the energy and a specific eigenstate, but I don't know the general form of eigenstates and eigenvalues, can I tell if the state is ground state or not?

What regulates the ground state energy of a hydrogen atom? Why is it constant (more or less)?

Homework Statement Calculate the energy of the electron in the ground state of triple ionized beryllium, which has an atomic number Z = 4. Homework Equations -Z2 (13.6) N2 The Attempt at a Solution Z=4 as given and it is tripled so our N=3. We throw our numbers in...

Homework Statement Consider a Hydrogen atom in the ground state Find: A- The Kinetic Energy, in eV B - The Potential Energy, in eV C - The Total Energy, in eV D - minimum energy required to remove the electron completely from the atom, in eV E - What wavelength does a photon with the...

Homework Statement Al3+ N3- Li+ Au+ Sr2+ Mn2+ Tl+ Br - Homework Equations The Attempt at a Solution no clue, the positives and negatives are messing me up

Homework Statement What are the energies of the ground state and the first two excited states of the He+ ion? Homework Equations En= - Eo/n2 The Attempt at a Solution n=1 for this problem (since there is only 1 electron) so the ground state would have the electron...

Homework Statement I just want to know if there is a relationship between the ground state of Hydrogen which is 13.6 eV and the ground state of Helium. The problem is asking me to find the ground state of Helium, but I am not sure how to go about it. Any advice? Homework Equations...

Homework Statement I have been given the Hamiltonian H = \sum_{k} (\epsilon_k - \mu) c^{\dag} c_k where c_k and c^{\dag}_k are fermion annihilation and creation operators respectively. I need to calculate the ground state, the energy of the ground state E_0 and the derivative...

This is what I've tried to work out and I'm not getting -13.7 eV. What am I doing wrong? E 2 Π m e^4 / (4 Π ε0 )^2 h^2 6.90E-19 J=4.31eV m 9.11 x 10-31 kg 9.11E-31 e 1.60 x 10-19 C 1.60E-19 ε0 8.85 x 10-12 C2/Nm2 8.85E-12 h 6.63 x 10-34 J S...

Homework Statement Seven electrons are trapped in a one dimensional infinite square well of length L. What is the ground state energy of this system as a multiple of h2 / 8mL2?Homework Equations Energy of a single electron in state n is n2h2 / 8mL2The Attempt at a Solution Pauli exclusion...

Hi everyone, This question is from my problem set this week in my Phys 371 class. Any help, hints or ideas would be very much appreciated! "Use the Heisenberg Uncertainty Principle to estimate the ground state energy in the hydrogen atom. Since the wave function that solves this problem is...

[SOLVED] Perturbed Ground State Wavefunction with Parity Homework Statement A particle is in a Coulomb potential H_{0}=\frac{|p|^{2}}{2m} - \frac{e^{2}}{|r|} When a perturbation V (which does not involve spin) is added, the ground state of H_{0} + V may be written |\Psi_{0}\rangle =...

so I had this thought earlier today. I am not claiming this is true or even likely but its interesting, possible (from everything I know), and may be testable by experiment. What if annihilation doesn't actually exist? What if what we see as an electron annihilating with a positron is...

Homework Statement Calculate the probability for finding the ground state harmonic oscillator beyond its classical turning points. Homework Equations Psi n(q) = (alpha/pi)^(1/4) exp(−alpha*q^(2)/2), where alpha = (kμ)^(1/2)/h bar The Attempt at a Solution i know it's going to be...

[SOLVED] Find the ground state energy [b]1. A particle is confined to a one dimensional box. Two possible state functions and the corresponding energies for the particles are shown in the figure. Find the ground state energy. EA=4eV EB=9eV Homework Equations...

Homework Statement Particle is in a tube with infinitely strong walls at x=-L/2 and x=L/2/ Suppose at t = 0 the electron known not to be in the left half of the tube, but you have no informations about where it might be in the right half---it is equally likely to be anywhere on the right side...

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...

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...