Ground state energy Definition and 60 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. J

    Ground State Energy of an Electron

    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...
  2. B

    Ground state energy of hydrogen atom

    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...
  3. S

    What Is the Ground State Energy of a Particle in a Box?

    [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...
  4. A

    Infinite Square Well Probability of getting Ground State Energy

    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...
  5. 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 =...
  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. 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...
  8. 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...
  9. 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...
  10. 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?
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