Ground state Definition and 275 Threads

The ground state of a quantum-mechanical system is its lowest-energy state; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state. In quantum field theory, the ground state is usually called the vacuum state or the vacuum.
If more than one ground state exists, they are said to be degenerate. Many systems have degenerate ground states. Degeneracy occurs whenever there exists a unitary operator that acts non-trivially on a ground state and commutes with the Hamiltonian of the system.
According to the third law of thermodynamics, a system at absolute zero temperature exists in its ground state; thus, its entropy is determined by the degeneracy of the ground state. Many systems, such as a perfect crystal lattice, have a unique ground state and therefore have zero entropy at absolute zero. It is also possible for the highest excited state to have absolute zero temperature for systems that exhibit negative temperature.

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  1. L

    Ground State of Quantum System: l=0?

    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...
  2. V

    How Many Unpaired Electrons in 1s2 2s2 3p1?

    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.
  3. E

    A question about the ground state wave function of XXZ model

    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.
  4. U

    Evaluate the ground state energy using the variational method

    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 =...
  5. T

    The ground state of the infinite square wel

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

    Ground State Energy of Diatomic Molecule

    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...
  7. W

    Need help fast Radial probablility density in ground state hydrogen

    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...
  8. C

    Excited atom decaying to ground state

    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...
  9. S

    Proving the Potential of Ground State Eigenfunction

    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...
  10. S

    3D harmonic oscillator ground state

    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...
  11. J

    What is the degeneracy of the ground state

    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...
  12. Repetit

    Ground state energy of free electron fermi gas

    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...
  13. L

    Maxwell field, ground state energy, 'The Universe in a Nutshell' help

    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...
  14. C

    Question regarding electronic ground state

    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?
  15. M

    What is the ground state energy of an electron? I thought i did this right

    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...
  16. Reshma

    What is the ground state of a particle with mass 'm' and potential V(x) = x^2?

    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?
  17. S

    Exploring the Ground State Energy: Harmonic Oscillator and Particle Description

    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...
  18. S

    Determining Ground State in L-S Coupling Scheme for (3d)4

    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...
  19. E

    Ground state energy of a vee-box using the uncertainty principle?

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

    Most probable value of r in ground state of hydrogen

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

    Deducing Terms from Period 2 Atom Ground State Configs

    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...
  22. Les Sleeth

    Does Light have a Ground State ?

    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...
  23. M

    <r> of hydrogen atom in ground state

    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...
  24. U

    Question about electrons moving from ground state

    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...
  25. N

    Why is the ground state eigenfunction in a symmetric hamiltonian also symmetric?

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