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.

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  1. R

    Fourier transform of t-V model for t=0 case

    To compute the Fourier transform of the ##t-V## model for the case where ##t = 0##, we start by expressing the Hamiltonian in momentum space. Given that the hopping term ##t## vanishes, we only need to consider the potential term: $$\hat{H} = V \sum_{\langle i, j \rangle} \hat{n}_i \hat{n}_j$$...
  2. ergospherical

    I Instability of hydrogen ground state if the time-reversal operator is unitary

    Apparently if we try to represent the time reversal operator by a unitary operator ##T## satisfying ##U(t)T = TU(-t)##, then the ground state of hydrogen (the hamiltonian of which is time-reversal invariant) is unstable. But if ##T## is anti-unitary (i.e. ##\langle a | T^{\dagger} T | b \rangle...
  3. 1

    Using Variational Principle to solve ground state energy

    First I picked an arbitrary state ##|ϕ⟩=C_1|φ_1⟩+C_2|φ_2⟩+C_3|φ_3⟩## and went to use equation 1. Realizing my answer was a mess of constants and not getting me closer to a ground state energy, I abandoned that approach and went with equation two. I proceeded to calculate the following matrix...
  4. W

    A Ground state of the one-dimensional spin-1/2 Ising model

    Hi, I know that the ground state of the spin-1/2 Ising model is the ordered phase (either all spin up or all spin down). But how do I actually go about deriving this from say the one-dimensional spin hamiltonian itself, without having to solve system i.e. finding the partition function? $$...
  5. P

    Why Does the Triangular Net Exhibit Three-Dimensional Properties?

    The answer for triangular net is -3NJ, so D=3, although I think that it has two dimensions in spite of every atom having three near neighbours.
  6. Diracobama2181

    I Ground State in Peskin and Schroeder

    In P&S, it is shown that $$e^{-iHT}\ket{0}=e^{-iH_{0}T}\ket{\Omega}\bra{\Omega}\ket{0}+\sum_{n\neq 0}e^{-iE_nT}\ket{n}\bra{n}\ket{0}$$. It is then claimed that by letting $$T\to (\infty(1-i\epsilon)) $$ that the other terms die off much quicker than $$e^{-iE_0T}$$, but my question is why is this...
  7. dRic2

    Ground state density requirement

    I've been think about it for hours but I'm really out of clue here... The only things I could think of are obvious or useless... Any help would be greatly appreciated.
  8. P

    A Antiferromagnetic ground state due to superexchange

    Hi all, thanks in advance for your help! For context, I'm generally new to condensed matter and many-body QM and am working through Altland and Simons' Condensed Matter Field Theory. I'm thinking in general about magnetic ordering. I've seen a Heisenberg-like spin Hamiltonian derived by...
  9. hilbert2

    A Ground state energy of a particle-in-a-box in coordinate scaling

    The energy spectrum of a particle in 1D box is known to be ##E_n = \frac{h^2 n^2}{8mL^2}##, with ##L## the width of the potential well. In 3D, the ground state energy of both cubic and spherical boxes is also proportional to the reciprocal square of the side length or diameter. Does this...
  10. eedftt

    What is the orbital radius of a muon captured in the n=1 ground state of Carbon?

    The muon is a subatomic particle with the same charge as an electron but with a mass that is 207 times greater: mμ=207me. Physicists think of muons as "heavy electrons." However, the muon is not a stable particle; it decays with a half-life of 1.5 μs into an electron plus two neutrinos. Muons...
  11. bob012345

    I Lithium Atom Ground State Radial Wavefunction

    I would like to see what the shape of the ground state radial wavefunction for the Lithium atom is. An approximate function that shows the shape would be fine. Thanks.
  12. hilbert2

    A Does Adding or Removing an Electron Change a Helium-3 Atom to a Boson?

    In the theory of superfluidity, ##^{4}##He atoms are seen as weakly interacting pointlike bosons, with an integer total spin. Does a ##^3##He atom also become a boson if I add or remove one electron to give ##^3##He##^+## or ##^3##He##^-## ? I'm trying to calculate the ground state wave...
  13. hilbert2

    A Ground state energy of cube-like potential wells

    In some other thread someone mentioned that a 3D cubic potential well always has a ground state that is a bound state, but a spherical well doesn't necessarily have if it's too shallow. I calculated some results for 3d cubes, spheres and surfaces of form ##x^{2n}+y^{2n}+z^{2n}=r^{2n}##, which...
  14. I

    Infinite Square Well Expansion: Mass m in Ground State

    A particle of mass m is in the ground state on the infinite square well. Suddenly the well expends to twice it's original size (x going from 0 to a, to 0 to 2a) leaving the wave function monetarily undisturbed. On answering, for ##\Psi_{n}## I got ##\Psi_{n}## = ##\sqrt{\frac{1}{a}}...
  15. L

    I Is the potential energy always negative in the ground state of a hydrogen atom?

    Why energy of the electron in ground state of hydrogen atom is negative ##E_1=-13,6 \rm{eV}##? I am confused because energy is sum of kinetic and potential energy. Kinetic energy is always positive. How do you know that potential energy is negative in this problem?
  16. Saptarshi Sarkar

    Ground state energy of 5 electrons in infinite well

    As the temperature given was 0K, I calculated the ground state energy of the system. I considered 2 electrons to be in the n=1 state, 2 in the n=2 state and 1 in the n=3 state by Pauli's exclusion principle. By this configuration, I got the total energy of the system in the ground state to be...
  17. jisbon

    Electron excited from the ground state to a quantum state

    Hi there, popping by here to check my answer because another online platform has already answered it but my answer appears to be wrong. I can't seem to understand why though :/ Since I can find the energy at a state to be ##E_{n}=\dfrac {-13.6z^{2}}{n^{2}}eV## At ground state where n=1...
  18. currently

    Deriving ground state electron energy using Boundary Value

    This is the equation given. I attempted to use Radial Equation, obtained from separating variables, to solve for ##E_1##.
  19. F

    I What happens if a low energy photon collides with an atom in the ground state?

    What happen if a small energy photon collide an atom in ground state that the gap between energy levels of atom is greater than energy of photon?It seems that the medium absorbs light and transform to heat?
  20. F

    I Why in BEC we must separate number of particles of ground state?

    In BEC, why do we separate the number of particles of ground state(E=0) from the integral(total number of particles) when temperature below critical temperature. Why is the overall integral wrong while the index of sum of number of particle can be considered as continuous? Is it correct that...
  21. Haorong Wu

    How to determine whether a state is a ground state

    I guess the hard way is to solve the Schrödinger equation, but that would be exhausting. I think the F-H theorem would not apply here. So do the Virial theorem. Are there other theorems I forget?
  22. binbagsss

    A Fractional Quantum Hall Effect- degeneracy of ground state (Tong's notes)

    Hi , I'm looking at the argument in David Tongs notes (http://www.damtp.cam.ac.uk/user/tong/qhe/three.pdf) for ground state degeneracy on depending on the topology of the manifold (page 97, section 3.2.4). I follow up to getting equation 3.31 but I'm stuck on the comment after : ' But such an...
  23. H

    A Overlap of nth QHO excited state and momentum-shifted QHO ground state

    ##\newcommand{\ket}[1]{|#1\rangle}## ##\newcommand{\bra}[1]{\langle#1|}## I have a momentum-shifting operator ##e^{i\Delta p x/\hbar}## acting on the ground state ##\ket{0}## of the QHO, and I want to compute the overlap of this state with the n##^{th}## excited QHO state ##\ket{n}##. Given...
  24. epotratz

    I Voltage between electron and proton in ground state hydrogen atom?

    I’m not sure if this belongs in classic or quantum physics... but here it is...Is it possible to calculate the “voltage” between an electron and a proton in a ground state hydrogen atom?I know the ionization energy is 13.6 eV, so I assume it's safe to say the voltage is 13.6 volts at a certain...
  25. JD_PM

    I Angular momentum of an Odd-Odd nucleus (in its ground state)

    What I know is the following: The total angular momentum of the nucleus is just the total sum of the angular momentum of each nucleon. If the nucleons are even the total angular momentum in the ground state will simply be ##0+##. If the odd number of nucleons is close to one of the magic...
  26. L

    A Quantum statistical canonical formalism to find ground state at T

    For my own understanding, I am trying to computationally solve a simple spinless fermionic Hamiltonian in Quantum Canonical Ensemble formalism . The Hamiltonian is written in the second quantization as $$H = \sum_{i=1}^L c_{i+1}^\dagger c_i + h.c.$$ In the canonical formalism, the density...
  27. thaiqi

    I Doesn't the atom in ground state radiate?

    According to textbooks, an atom in ground state doesn't radiate. Yet I got some other idea after reading Wu Ta-you's theoretical physics book. I hold the viewpoint that the atom does radiate, and at the same time it absorbs energy from heat radiation in its environment. The energy it radiates...
  28. C

    I Confusion on binding energy and ionization energy.

    1) I know that the binding energy is the energy that holds a nucleus together ( which equals to the mass defect E = mc2 ). But what does it mean when we are talking about binding energy of an electron ( eg. binding energy = -Z2R/n2 ? ). Some website saying that " binding energy = - ionization...
  29. O

    Statistics physics problem -- atom is in the ground state or excited state?

    I am learning for my exam in particle physics. One topic is statistical physics. There I ran into this question: Consider an atom at the surface of the Sun, where the temperature is 6000 K. The atom can exist in only 2 states. The ground state is an s state and the excited state at 1.25 eV is a...
  30. S

    Total energy of hydrogen at ground state

    Homework Statement What is the total energy of the hydrogen atom at ground state? a. 13.6 eV b. mpc2 + mnc2 c. mpc2 + mnc2 - 13.6 eV d. mpc2 + mnc2 + 13.6 eV Homework Equations E =...
  31. C

    Ground state and 1st excited state energy of 3 Fermions

    Homework Statement So in my problem, there's a given of 3 non interacting fermions in a harmonic well potential. I already got the wavefunction but i have problems in obtaining the ground state energy and its 1st excited state energy for 3 fermions (assuming they are non interacting and...
  32. D

    Energy Difference with a Two Delta Function Potential

    Homework Statement Consider a particle of mass m moving in a one-dimensional double well potential $$V(x) = -g\delta(x-a)-g\delta(x+a), g > 0$$ This is an attractive potential with ##\delta##-function dips at x=##\pm a##. In the limit of large ##\lambda##, find a approximate formula for the...
  33. L

    I Estimate of ground state energy for the Yukawa potential

    I’ve seen the uncertainty principle used to calculate the ground state energy for things like hydrogen and the harmonic oscillator, but can this be done for the Yukawa potential where you have an exponential?
  34. J

    I Is the Smallest Eigenvalue Always the Ground State Energy?

    If I diagonalize the hamiltonian matrix ,I can get the eigenvalues , does the smallest eigenvalue always be the ground state energy?
  35. N

    Is this really an excited state?

    The figure below is from a textbook. It is explaining what excited states are using carbon as an example. I don't necessarily agree that the the state labeled as "example excited state 1" is really an excited state. Since the electrons in the 2p orbitals are unpaired, and in the absence of a...
  36. Warda Anis

    Expectation value <p> of the ground state of hydrogen

    Homework Statement How should I calculate the expectation value of momentum of an electron in the ground state in hydrogen atom. Homework Equations The Attempt at a Solution I am trying to apply the p operator i.e. ##-ihd/dx## over ##\psi##. and integrating it from 0 to infinity. The answer I...
  37. A

    A The half harmonic oscillator's ground state wave function

    For the half harmonic oscillator the ground state wave function is of the form x*exp(-x^2/2) But sir how to check it's parity and with respect to with point As this function is valid for positive x only Thank you
  38. Sushmita

    Ground state energy of 5 identical spin 1/2 particle

    Homework Statement The ground state energy of 5 identical spin 1/2 particles which are subject to a one dimensional simple harkonic oscillator potential of frequency ω is (A) (15/2) ħω (B) (13/2) ħω (C) (1/2) ħω (D) 5ħω Homework Equations Energy of a simple harmonic oscillator potential is En...
  39. Sushmita

    A particle of mass 'm' is initially in a ground state of 1- D Harmonic oscillator potential V(x)....

    Homework Statement [/B] A particle of mass 'm' is initially in a ground state of 1- D Harmonic oscillator potential V(x) = (1/2) kx2 . If the spring constant of the oscillator is suddenly doubled, then the probability of finding the particle in ground state of new potential will be? (A)...
  40. J

    I Is the ground state energy of a quantum field actually zero?

    I start by outlining the little I know about the basics of quantum field theory. The simplest relativistic field theory is described by the Klein-Gordon equation of motion for a scalar field ##\large \phi(\vec{x},t)##: $$\large \frac{\partial^2\phi}{\partial t^2}-\nabla^2\phi+m^2\phi=0.$$ We...
  41. RicardoMP

    Ground state of 3 noninteracting Fermions in an infinite well

    In Zettili's Quantum Mechanics, page 477, he wants to determine the energy and wave function of the ground state of three non-interacting identical spin 1/2 particles confined in a one-dimensional infinite potential well of length a. He states that one possible configuration of the ground state...
  42. neilparker62

    I Exploring the Ground State Lamb Shift: Advances and Controversies

    What exactly is the so-called "Ground State Lamb Shift". It seems to have been an 'in vogue' quantity up till 1995 or so - then vanished from the literature ?? It's the 'self energy' or something like that of an electron in H 1S orbital. A scientist (at NIST) told me it's a term that has gone...
  43. A

    I Ground State Energy of a Potential: λ2px2/2m+0.5kx2

    I am having a doubt that if Id lho potential is Given of the form λ2px2/2m+.5kx2 then whether the ground state energy of the system is λ2/4ħω+1/4ħω
  44. D

    I 2D LHO calculate ground state energy

    A question I have faced in exam to calculate ground state energy Given Hamiltonian 1/2m(px2+py2)+1/4mw2(5x^2+5y^2+6xy) ground state energy has to be obtained Its clear that the Hamiltonian is a 2D LHO Hamiltonian but what for the term 3/4(x+y)2
  45. S

    A Is there an alternative form of the zero point energy?

    Hi, is there an alternative form of the zero point energy for free electrons, where there is no space interval L to be quantized in? The zero point energy for electrons in an atom can be simplified to a variant where Z^2 is present in the nominator, however, these are not free electrons. Can a...
  46. TheBigDig

    Expectation value of mean momentum from ground state energy

    1. The problem statement Consider a particle of mass m under the action of the one-dimensional harmonic oscillator potential. The Hamiltonian is given by H = \frac{p^2}{2m} + \frac{m \omega ^2 x^2}{2} Knowing that the ground state of the particle at a certain instant is described by the wave...
  47. WeiShan Ng

    I Why drop the vibrational ground state energy

    This is from *Statistical Physics An Introductory Course* by *Daniel J.Amit* The text is calculating the energy of internal motions of a diatomic molecule. The internal energies of a diatomic molecule, i.e. the vibrational energy and the rotational energy is given by...
  48. hilbert2

    A Several ground state calculations at once

    Suppose I want to find the ground states corresponding to several Hamiltonian operators ##\left\{ \hat{H}_i \right\}##, which are similar to each other. As an example, let's take the ##\hat{H}_i##:s to be anharmonic oscillator Hamiltonians, written in nondimensional form (##\hbar = m = 1##) as...
  49. Arup Biswas

    B How do electrons behave when energy is added to an atom's ground state?

    Yah electrons existing the lowest possible energy state! Now suppose, we throw a beam of light towards a ground state of a atom. I heard/know electrons will take up energy from the photon "hv", and go to the next energy level i.e. excited state. Now my point is, is it only the valance electron...