What is Ground state: Definition and 275 Discussions

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.

View More On Wikipedia.org
Recent contents Top users
  1. alemsalem

    Symmetry breaking and the ground state of a quantum field theory.

    when a continuous symmetry is broken, we say that the ground state is just one of the possible ground states, and there is no energy cost in moving from one to the other.. why doesn't the state keep changing with the slightest perturbation (production of goldstone boson). why don't we have a...
  2. K

    Can light excite an electron from ground state to a higher state?

    can "light" excite an electron from ground state to a higher state? An electron of a particular atom can absorb a discrete amount of energy, leap to a new quantum level, and then jump back down to lower states (emitting photons). My understanding is that going from n=2 to the ground state a...
  3. T

    Removing an electron out of the ground state

    Homework Statement How much energy (in kJ) does it require to remove an electron out of the ground state of hydrogen atom completely, according to Bohr? Homework Equations The Attempt at a Solution
  4. T

    Ground State Energy of Helium Atom - Integration problem

    I'm trying to follow a derivation of the ground state energy of Helium using perturbation theory. I've made it through most of the derivation but I'm stuck at the following integral Homework Statement Find the value of C where C=\frac{1}{(4\pi)^2}\int...
  5. L

    Finding Ground State Wave Functions: Tips & Tricks

    Hi, If I have the Hamiltonian: H=(1/2)p^2+(1/24)\lambda(x^2-v^2)^2 what is the best way to find the ground state wave functions \psi(x) . I was thinking this sort of looks like the harmonic osscilator, so maybe a clever change of variables could do the trick? or some form of perturbation...
  6. H

    Write down the ground state eigenfunction (and spin) of Helium.

    Homework Statement Already it is on title ! Homework Equations attachents provide the most relevant equations i could find. The Attempt at a Solution I have found some old books written in 1920 decade ,dealing with this subject,but the solution they provide seems very hard...
  7. B

    Determine the ground state energy

    Homework Statement A particle of mass m is confined to move in a one-dimensional "infinite" potential well defined by V(x)=0, |x|< or=a, V(x)=infinity otherwise. The energy eigenvalues are E(subscript n)=((n^2)(pi^2)(h-bar^2))/(8m a^2), with n=1,2,3,... and the orthonormal eigenfunctions are...
  8. E

    Ground state radiation question

    I had a curious thought today, here is my logic: Charged particles have E fields. Moving charged particles create B fields. Electrons are moving charged particles, oscillating in an atom. Therefore, I concluded that an atom must be creating an oscillating EM wave, even in the ground state. But...
  9. T

    Eigenvalues and ground state eigenfunction of a weird Hamiltonian

    Hello again everyone! I would like to ask a question regarding this Hamiltonian that I encountered. The form is H = Aa^+a + B(a^+ + a). Then there is this question asking for the eigenvalues and ground state wavefunction in the coordinate basis. The only given conditions are, the commutator...
  10. C

    Uncertainty in Energy an ground state energy

    I'm asked to show that in the ground state, a particle trapped in a potential well approximately equal to its lowest allowed energy. I know the expression for the energy is h^2/8mL^2 for a finite well, and ΔEΔt~h/2π. But I'm at a loss as to how I'm supposed to even begin to start this...
  11. W

    Using uncertainty principle to estimate ground state energy

    Homework Statement Use the uncertainty principle to estimate the ground state energy of a particle of mass "m" is moving in a linear potential given by V(x) = ∞ for x≤ 0 V(x) = αx for x ≥ 0 Homework Equations ΔxΔp ≥ h/2 The Attempt at a Solution I've looked at a similar problem...
  12. M

    Ground state oscillation freq. of H2?

    Does anyone have the most up-to-date zero-point oscillation frequency for a hydrogen molecule? This is not a homework question, I'm thinking about incorporating it into a tattoo someday. I don't wish to have a tattoo with inaccurate info, so any help would be appreciated.
  13. M

    Hydrogen atom in ground state: some puzzle

    I noticed many PF threads mention ground state of Hydrogen atom. At the same time it is two body problem considered to be solved by separation of variables. It is true, of course, that we can find basis wave functions (solutions of Shroedinger equation). But why does anybody think, that...
  14. M

    1D Ising ground state

    Homework Statement Find the ground state (stable configuration at T = 0) of the one-dimensional ising model with first and second neighbour intercations: H = -J_1 \sum_{i} s_i s_{i+1} -J_2 \sum_{i} s_i s_{i+2} where s_i = \pm 1 The Attempt at a Solution I really don't know what i...
  15. P

    Ground state energy and wavefuntion?

    Homework Statement Find the ground state energy and the ground state wavefunction for a particle of mass m moving in the potential V=\frac{1}{2}mw^{2}x^{2} at x>0 V=\infty at x<0 The Attempt at a Solution Well, the problem I am having is that I have answering questions that always...
  16. S

    Atomic Ground State: What Is It?

    Homework Statement Hey guys, I'm studying AS level physics at the moment in the UK and I'm having a hard time grasping the concept of the ground state of an atom, so my question is: Is the ground state the energy level that is closest to the atoms nucleus or is it the energy level that a...
  17. P

    Transition of neon from ground state to excited state

    Neon has lowest excited energy at 1(s^2)2(s^2)2(p^5)3(s^1) state. And the excitation energy is about 16.9eV. And next energy is at 1(s^2)2(s^2)2(p^5)3(p^1) state. And the excitation energy is about 19eV. In Franck Hertz experiment with Neon, current decrease at every 19eV, no 17eV. Why...
  18. B

    Griffiths QM Ground State of Harmonic Oscillator

    Homework Statement Folks, I am looking at a past exam question regarding the Harmonic Oscillator. The question ask 'Justify that the ground state of a harmonic oscillator a_\psi_0=0 equation 2.58 on page 45 of griffiths. THis was not covered in my notes. Any ideas how to justify this...
  19. C

    Question: Minimum uncertainty in ground state electrons

    Hey all, I'm a student curently studying in a Singaporean Junior College (American 12th grade equivalent). I was curious and just thought of the following: Suppose a system with a electron and a proton nucleus, a hydrogen atom. From electrostatic force and circular motion equations- F =...
  20. N

    SHO in 2D - ground state energy

    Homework Statement A two-dimensional harmonic oscillator is described by a potential of the form V(x,y) = 1/2 m \omega^{2}(x^{2}+y^{2} + \alpha (x-y)^{2} where \alpha is a positive constant. Homework Equations Find the ground-state energy of the oscillatorThe Attempt at a Solution I have tried...
  21. H

    Calculating Sodium Atom Ground State Degeneracy

    Hi guys, Just got a question I'm a little stuck on and would love a push in the right direction Q) Using Hartree's theory calculate the degeneracy of the ground state of the Sodium atom. Its a previous exam question and I'm struggling to find much descriptive information about the topic...
  22. B

    Probability of measuring the ground state of a particle (quantum mechanics)

    Have to find the probability of measureing the ground-state energy of a particle. -in infinite potential well 0<x< a has wave-function \psi (x,0) = Ax(a-x) where a is the (known) length of the well, and the norm. const. A has already been found. The eigenvalues of the hamiltonian in...
  23. T

    Quantum Mechanics - Ground State of Helium Atom

    I have confused myself with this by reading a combination of Wikipedia, books and my QM notes and I'm afraid I need someone to untangle me please. Basically what I want to know is, what are the consequences of the Pauli exclusion principle for the ground state of the helium atom? Here's my...
  24. D

    Aproximate ground state wave functions

    Homework Statement So to test the variational method of simple harmonic oscillator I am using some functions that can be a good approximations, such as: Gaussian: \psi(x)=Ae^{-bx^2} Polynomial: \psi(x)=1-bx^2+\frac{b^2 x^4}{2} (I just expanded the Gaussian into Taylor, I can use just...
  25. B

    Estimating the energy of the ground state of a harmonic oscillator from the

    uncertainty relation. I think I'm on the right track. Currently, I'm at, E = (1/2m)*<p^2> + (1/2)*k*<x^2> and when applying the uncertainty relation, deltax = <x^2>^(1/2) deltap = <p^2>^(1/2) How do I go about connecting everything from here? Thanks!
  26. K

    Ground state of harmonic oscillator

    Homework Statement Verify that the ground state (n=0) wavefunction is an eigenstate of the harmonic oscillator Hamiltonian. Using the explicit wavefunction of the ground state to calculate the average potential energy <0|\hat{v}|0> and average kinetic energy <0|\hat{T}| 0> Homework...
  27. D

    Final |L,S> states after ground state pionic atom (spin 1) decays into two neutrons

    Homework Statement A pion is a spin-0 particle with a negative unit charge. A neutron is a spin-1/2 particle with no charge. A proton is a spin-1/2 particle with positive unit charge. One can construct an unstable version of the hydrogen atom where the nucleus contains both a proton and a...
  28. D

    Bohr Radius and Ground State Energy

    Homework Statement Given the potential energy V(r)=-\frac{1}{4\pi \epsilon_0}\frac{e^2}{r} (where e is the unit charge), use the uncertainty principle \Delta x \Delta p \geq \hbar to find the Bohr radius r_B for a hydrogen atom and the ground state energy E_0. Hint: write down the kinetic...
  29. A

    Finding the ground state energy of electron

    1) The problem is about finding the ground state energy of electron in an infinite 2D circular and square potential well with the same area. I have calculate it via method of separation of variables in polar and cartesian coordinate respectively, and it is found out that the one on the circular...
  30. K

    Ground state wavefunction real?

    Hi.. In a textbook, the ground-state wavefunction for any general Hamiltonian was under consideration. Then, a statement was made that this wave function is real since it is the ground state. Is it true that one can always choose the ground state wave function to be real? I understand...
  31. M

    Ground state energy of nucleus

    How do we compute the energy of the ground state using nuclear shell model?
  32. S

    Can anyone confirm the ground state Bohr radius for muonic hydrogen?

    Thanks in advance for anybody who is kind enough to help me. No this isn't for my homework. I am not even enrolled in school. I am doing some calculations for personal research. But I need to know the ground state radius of a muonic hydrogen atom to help prove my theory. I already know the...
  33. S

    Ground state magnetic moment of 7Li

    Homework Statement Calculate the ground state magnetic moment of 7Li using the below equations. The spin value is 3/2. Homework Equations mu_J = gamma_J * J* hbar = g_J * u_N with g_J = [g_l + (g_s - g_l)/(2l + 1)] where g_l and g_s are orbital and intrinsic spin g factors for...
  34. P

    Classical ground state is Ne\'{e}l state:

    Tha classical ground state is Ne\'{e}l state: every spin up is surrounded by nearest neighbours which are down, and vice versa. To give them a name, denote the spins down the A sublattice, and the spins up the B sublattice. Perform a canonical transformation on the B (but not on the A spins...
  35. P

    Muonic hydrogen ground state energy

    Would the energy just be a multiple of how much bigger it is than electron?
  36. O

    Ground State Parity in One-Dimensional Potentials

    Must the ground state in an even potential of one dimension be the even parity?
  37. B

    Spectroscopic term of ground state electron configuration of Carbon atom

    The ground state electron configuration of Carbon atom is 1s^{2}2s^{2}2p^{2} For the electrons, 1s^{2}2s^{2}, L=0, S=0 So only consider electrons of 2p^{2}, and s_{1}=s_{2}=1/2 ---> S=0,1 l_{1}=l_{2}=1 ---> L=0,1,2 For S=0, L=0; J=0, so we have ^{1}S_{0} For S=0, L=1; J=1, so...
  38. I

    Analyzing a Finite Potential Well: Estimating Ground State Energy

    Homework Statement An electron is confined to a potential well of finite depth and width, 10^-9 cm. The eigenstate of highest energy of this system corresponds to the value \xi = 3.2. a. How many bound states does this system have? b. Estimate the energy of the ground state with respect...
  39. K

    Total ground state energy of N fermions in a 3D box

    Hello everybody, I just have no idea how to start this problem so i was hoping you guys would point me in the right direction and then i'll be able to go on by myself the problem asks to show that the total ground state energy of N fermions in a three dimensional box is given by E total =...
  40. M

    Finding the Ground State of a Hamiltonian Operator

    When given a Hamiltonian operator (in this case a 3x3 matrix), how do you go about find the ground state, when this operator is all that is given? By the SE when have H\Psi=E\Psi. I can easily solve for Eigenvalues/vectors, but which correspond to the ground state, or am I missing something?
  41. F

    Perturbation Theory - Shift of Ground State

    Homework Statement Use leading order perturbation theory to calculate the ground state shift of hydrogen due to perturbation: \hat{V} Homework Equations 1. Leading terms in expansion of energy: E=mc^{2}+\frac{p^{2}}{2m}-\frac{p^{4}}{8m^{3}c^{2}}+... 2. \hat{H}=\hat{H}_{0}+\hat{V} where...
  42. W

    Schrodinger ground state wave function

    Homework Statement Find the ground state wave function for the 1-D particle in a box if V = 0 between x = -a/2 and x = a/2 and V = \infty Homework Equations I would guess -- Schrodinger's time-independent equation...
  43. Shackleford

    Calculate probability electron remains in ground state of He3.

    I'm not sure how to calculate the probability in a non-hydrogenlike atom. Perhaps I'm missing something. Z=1 to Z=2. Of course, n, the principal quantum number is n and l would be zero. http://i111.photobucket.com/albums/n149/camarolt4z28/2010-09-23195548.jpg?t=1285517610
  44. J

    Symmetry of the Bloch Ground State

    I was reading Hasan & Kane's review on topological insulators and right in the beginning, page 3, they say that the Bloch ground state is U(N) invariant. I do not see that. Would anyone be able to show it or point to a reference? Thanks, Jan.
  45. atyy

    Is the ground state in LQG a coherent state?

    As I understand, it is postulated that only coherent states in LQG correspond to classical spacetimes. Is the ground state of LQG a coherent state? Otherwise, what principle selects that the universe should be in a coherent state?
  46. A

    Ground state properties of Hubbard model

    Hello everyone, I want to know the presently existing works on the topic of ground state properties of Hubbard model (spin-1/2-, or extended- ). I am nonexpert and have not googled for useful information. Please tell me some articles or monographs on this if you know. Thanks!
  47. D

    Bose-Einstein-Condensate ground state energy E_0 = 0

    Hi, why is the ground state energy usually set to E_0 = 0 for a Bose gas? Normally one looks at a particle in a box, where the ground state energy should be different from 0. Here is the "particle in a box ground state energy" calculated in a Bose-Einstein contex...
  48. LarryS

    What are null oscillations in quantum systems?

    What does the Ground State of a quantum simple harmonic oscillator represent physically? Thanks in advance.
  49. T

    Experimental determination of ground state configuration

    Ok so I've been wondering, how is it that physicist's EXPERIMENTALLY determine the ground state configuration of electrons in a particular atom? In other words do they use emission spectra/thermodynamic calculations/etc? Also, if ground state represents an atom's minimal energy state, which...
  50. S

    Probability of finding a particle in the ground state

    Homework Statement A particle is prepared in the state \psi (x) = \frac{1}{\sqrt{L}} in a region 0 < x < L between two hard walls (particle in a box). Calculate the probability that the particle is found in the ground state when its energy is measured. Homework Equations This question...
Back
Top