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. N

    Kinetic energy of a hydrogen atom in its ground state

    Homework Statement While playing around with basic QM, I tried using the hamilton operator to find the kinetic energy of a hydrogen atom in its ground state. I assume the wave function ##\psi_1## is known. However, I of course ran into problems... 1) in my solution attempt below, I end up with...
  2. S

    Probability to find electron in ground state

    Homework Statement An electron in hydrogen atom can be described with normalized wavefunction ##\psi (r,\vartheta ,\varphi )=(\frac{1}{64\pi r_B^3})^{\frac{1}{2}}exp(-\frac{r}{4r_B})##. Calculate the probability that the electron is in ground state of hydrogen atom. How much is the energy...
  3. W

    What causes an electron to return to its ground state?

    I've recently realized I have completely taken for granted that electrons simply tend to be found in their ground state. I want to understand fundamentally what is causing the electron to drop back to its ground state. It feels a force from the positively charged nucleus, but if it was given...
  4. U

    Ground state of harmonic oscillator

    Shouldn't the integrating factor be ##exp(\frac{m\omega x}{\hbar})##? \frac{\partial <x|0>}{\partial x} + \frac{m\omega x}{\hbar} <x|0> = 0 This is in the form: \frac{\partial y}{\partial x} + P_{(x)} y = Q_{(x)} Where I.F. is ##exp (\int (P_{(x)} dx)##
  5. R

    Does the Dirac ground state of the H atom have an electron current?

    I have confounded myself with the following observation. Take the standard expression for the lowest energy Dirac 4-spinor solution of the Dirac equation with a Coulomb potential (the H atom ground state). Plug this into the standard expression for the 4-vector current and use values for the...
  6. G

    Unbounded Hamiltonian leading to finite ground state

    If a Hamiltonian is unbounded from below, say the hydrogen atom where the Hamiltonian is -∞ at r=0, is there a way to tell if the ground state is bounded (e.g. hydrogen is -13.6 eV and not -∞ eV)? It seems if the potential is 1/r^2 or less, then the energy will be finite as: \int d^3 r (1/r^2)...
  7. Z

    How do you calculate the magnetic moment of the ground state of Calciu

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  8. Q

    Ground State of the Simple Harmonic Oscillator in p-space

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  9. S

    Ground State Degeneracy in ferromagnetic Heisenberg model

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  10. A

    Does the Ground State of a Bose Gas Have Zero Entropy?

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  11. F

    E-field Perturbation of 2D rotor. Show Y_10 couples ground state?

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  12. D

    Electron far away from the nucleus of ground state H atom

    The wave function of an electron in ground state hydrogen atom is non-zero at points far away from the nucleus. Interpreted as the probability of finding the electron, this is telling us that there is a finite probability of finding an electron far away from the nucleus even if it is at ground...
  13. M

    Why is Vanadium 4s2 3d3 in its ground state?

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  14. O

    Value of L for the ground state of Vanadium (II)

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  15. D

    Total angular momentum of atom in its ground state

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  16. F

    The radial probability density for the hydrogen ground state

    Is there an experimental verification of the radial probability density for the hydrogen ground state given in the introductory texts. See the following link as an example. Thank you in advance. http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydrng.html#c1
  17. Roodles01

    Expectation value in the ground state

    Homework Statement . Hi, could someone look at the attachment & comment on whether I'm anywhere near getting the expectation value correct, please. In the grnd state; 1. terms such as AA†A†A, with lowering operator on RHS has zero expectation value, 2. terms such as AA†A†A† with uneven...
  18. tomwilliam2

    Operators on a Harmonic oscillator ground state

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  19. Roodles01

    Expectation value at ground state

    I realize that at ground state of a harmonic oscillator the energy will be at zero. I'm assuming that the expectation value will also be at zero. Could someone confirm this & possibly explain just a little more. Thank you
  20. H

    Molecular material ground state

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  21. N

    How can a ground state of free particles have entanglement?

    Can somebody clear the fog in front of my eyes: how can a Hamiltonian describing free fermions have a ground state with non-trivial entanglement? My reasoning is: we can build the ground state in the independent electron approximation (which is now exact), hence it is a product state in the...
  22. C

    How to find the ground state of He atom

    Hello PF members, I am trying to solve for helium atom ground state by using perturbation theory. It is very easy to calculate the first order correction of ground state energy but I have no idea for how to find its wave function. I have tried to use the first order correction formula for wave...
  23. L

    Does the ground state wave function in QM problems have any zeros?

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  24. S

    QFT Ground State Analysis: Understanding e^(-iHT) |0>

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  25. P

    Number operator in the ground state

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  26. R

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  27. S

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  28. J

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  29. L

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  30. N

    Energy of H Atom in 1st Excited State - 23.8 eV

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  31. M

    Infinite Square Well Electron Jumps from n=4 to ground state

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  32. B

    Dark Matter as possible ground state for all matter

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  33. G

    What is the Energy of a Photon Released in Atom Decay with a Change in Mass?

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  34. S

    Prove Heisenberg Uncertainty Principle for Ground State Harmonic Oscillator

    Ground State Wave Equation: ψ0=(a/∏)(1/4)e(-ax2/2) Prove the Heisenberg Uncertainty principle ≥h(bar)/2 by way of expectation values. First I found <x>=0 because it was an odd function then I found <Px>=0 because it was an odd function Then <x2>=∫(a/∏)(1/2)x2e(-ax2)/2dx=1/2a by way of...
  35. PerpStudent

    Experimental evidence for the ground state of energy

    I hope this is a coherent question: Solving the Schrödinger equation for energy eigenvalues for a harmonic oscillator leads to the ground state of the energy for a particle being ω/2. What is the experimental evidence that this is, in fact, the lowest achievable energy and that zero energy is...
  36. E

    Deuteron Ground State / Perturbation Theory

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  37. I

    Transformation function from ground state -> nth energy state, force applied, HO

    Hello Everyone! I have a question regarding a Quantum problem I am trying to solve in L. Brown's Quantum Field Theory book, Chapter 1, Problem 4.f. Homework Statement I have a question which asks me to compute [p][/n], i.e. the probability that the ground state (n=0) is brought to the...
  38. W

    Why an atom can have nonzero toal angular momentum in the ground state?

    In its ground state, an atom has no net electric dipole momentum ,but it can have a nonzero angular momentum. Is this a spontaneous symmetry breaking? why the ground state is not of zero angular momentum?
  39. Spinnor

    A jump rope in the ground state gets excited.

    Say two girls spin a jump rope, of length ∏ meters, so that the only nodes are where the girls hold the rope, ψ= sin(x)exp(iω_1t) (actually there are no nodes at the girls hands as where they hold the rope goes in a smallish circle). Now instruct the girls how to shake the rope so as to most...
  40. S

    Helium ground state questions

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  41. W

    Two-electron Ground State of a Spin-Independent Hamiltonian is a singlet

    Homework Statement The problem is from Ashcroft&Mermin, Ch32, #2(a). (This is for self-study, not coursework.) The mean energy of a two-electron system with Hamiltonian \mathcal{H} = -\frac{\hbar^2}{2m}(∇_1^2 + ∇_2^2) + V(r_1, r_2) in the state ψ can be written (after an integration by...
  42. R

    Ground State Energy for infinte potential well

    Homework Statement A particle of mass (m) moves in the one-dimensional potential V(x) = V0 0 ≤ x ≤ a = ∞ otherwise Wave function of the particle is ψ(x,t) = C sin (\frac{x\pi}{a}exp[-iωt] Determine V0 Homework Equations Schrödinger's Equations...
  43. T

    Interpretation of quantum fields and their ground state energies.

    Quantum field theory predicts a value for the cosmological constant that is 123 orders of magnitude larger than the observed value (if one assumes the Standard Model to be correct up to the Planck scale of 10^19 GeV)! To theoretically predict the value of the cosmological constant, one must, I...
  44. D

    Bohr model question - transition between first excited state and ground state

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  45. L

    Ground state energy of particle in quantum harmonic oscillator.

    Homework Statement Consider a quantum mechanical particle moving in a potential V(x) = 1/2mω2x2. When this particle is in the state of lowest energy, A: it has zero energy B: is located at x = 0 C: has a vanishing wavefunction D: none of the above Homework Equations The...
  46. S

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  47. M

    Representation theory and totally symmetric ground state?

    Hello My question is about the ground state of vibrations for a solid. I'm working with graphite and have found out that for k=0 (The Gamma symmetry point), the vibrational modes can be decomposed into irreducible represenations in the following way Vibration = 2 * E1u + 2 * E2g + 2 * A2u...
  48. L

    Magnetic moment of proton and electron of H-atom in ground state L=0

    Homework Statement Consider the Hydrogen atom in a magnetic field of 2T. If the atom is in its ground state (orbital angular momentum L=0): (a) Write down the magnetic moments of the proton and the spinning electron. [1]Homework Equations I am aware that the magnetic moment μ =...
  49. maverick280857

    Is the ground state of a harmonic oscillator unique?

    Hi, In one of my advanced quantum mechanics classes, the instructor posed a problem, namely to show that the ground state of a one dimensional quantum harmonic oscillator is unique, without getting into differential equations. I know that the equation a\left|0\right\rangle = 0 when...
  50. S

    The Hydrogen Atom Ground State: Radiation Emission

    when proton and electron combine to form hydrogen atom(ground state) what is the source of radiation emitted
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