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. D

    Ground state hydrogen parallel to the double slit experiment?

    In the double slit experiment the electron can go through either slit. As long as it is not observed there is an interference pattern as the two possibilities superimpose. The common conclusion to this is that the electron goes through both slits. Is there a parallel with the ground state...
  2. A

    Momentum four vector for ground state.

    I am confused about the definition of ground state and its characteristics. For a field in spacetime do we mean the ground state to be the minimum of the potential or minimum of the total energy? Specifically what is the momentum four vector of the ground state ( p^{\mu}=(...) ) for a massive...
  3. L

    How to show the ground state is orthagnol with the first in a quantum harmonic os

    How to show the ground state is orthagnol with the first in a quantum harmonic os... Homework Statement This is a revision question for an upcoming quantum mechanics exam, that i am stuck on. Any help or idea at how to approach the question would be greatly appreciated, i get the feeling...
  4. R

    Mass Defect of Hydrogen-2 Electron Binding Energy

    Homework Statement : the binding energy for the electron in the ground state of hydrogen-2 is 13.6ev what is the corresponding mass defect of the hydrogen atom in amu (atomic mass units) not sure if you need atmoic mass of the hysgrogen atom its given to be 2.014102u Relevant equations: not...
  5. M

    Perturbation Theory & the Ground State in a 1-D Potential Box

    A particle is in the ground state in a one-dimensional box given by the potential v(x)= 0 for 0<x<a v(x)= inifinity other wise A small perturbation V = V(0)x/a is now introduced. Show, correct to first order in perturbation theory, hat the energy change in the ground state is V(0)/2...
  6. G

    Determining Ground State of an Atom: Pauli, Hunds, Coloumb's Rules

    im looking for the 3 principals i need to be employ in determining the electronic structure of the ground state of an atom Ive got Paulis exclusion principle where no 2 electrons in an atom can occupy the same quantum state and hunds rule of the total spin of the electrons always has it...
  7. V

    How many electrons in the ground state of a Hg atom

    How many electrons in the ground state of a Hg atom can have the quantum number ml = +1? The way I am trying to figure this out is as follows.. Electron configuration for HG is.. [Xe]6s^2 5d^10 n=6 l : ml 0: 0 1: -1,0,1 2: -2,-1,0,1,2 3 -3,-2,-1,0,1,2,3 4 -4,-3,-2,-1,0,1,2,3,4...
  8. J

    Quantum mechanics ground state

    Why must the ground state not have a node？ And the first excited state must have 1 node.
  9. J

    Why is the ground state always symmetric?

    Homework Statement Why is the ground state always symmetric and first excited state anti-symmetric? OR Why does the ground state always have no node and first excited state has one node? Homework Equations The Attempt at a Solution
  10. Oddbio

    What is the ground state wave function of ortho-helium and its degeneracy?

    I want to construct the ground state wave function of orthohelium. Here is my reasoning, please let me know if I am correct or not. I forgot to add that for this post I am ignoring the electron-electron interactions. Orthohelium has the triplet spin state which is symmetric. Because the total...
  11. S

    Ground state wavefunction & energy for 2 electrons

    Homework Statement 2 electrons are in a box of length L. Ignoring Coulomb force, 1 and 2 are labels for the electrons and m is the mass of an electron. What is the ground state and 1st excited state for the energy and wavefunction for the two electrons? Is there more than one wavefunction...
  12. T

    Hydrogen Ground State Energies - Question

    I am an A-level teacher so I don't want an answer in terms of anything too complicated (for my students!) The hydrogen atom has a ground state energy of -13.6eV. I am happy with this. This means that the electron needs 13.6eV of kinetic energy in order to become free of the nucleus...
  13. C

    Is the Ground State Quantum Number n Equal to 0 or 1?

    Homework Statement when using E=(h(pi)n)^2/(2mL) h=h bar m= mass of particle L= length this may be a dumb question but is the ground state 0 or 1 for n n=0,1,2...
  14. Q

    Ground state energy of a two particle gravitational atom

    Homework Statement Two neutral spinless particles of mass m are gravitationally bound to one another. What is the ground state energy of this two-particle gravitational atom? Homework Equations The Attempt at a Solution So, it's a two particle system, but H_{total} = H_1 +...
  15. S

    Estimate ground state energy with HU

    Hi, i worked through several examples where the ground state energy of a particle in an arbitrary potential V(r) is estimated with Heisenberg's uncertainty relation. In these examples they prepare the Hamiltonian for the particle. For example the Hamiltonian for a particle in a harmonic...
  16. R

    Using Hund's rules to calculate ground state of erbium

    Homework Statement Calculate ground state of erbium [Xe] 4f^12 6s^2 The Attempt at a Solution so i know that the f orbital can hold 14 electrons and has 7 types of orbitals that is -3,-2,-1,0,1,2,3 So i constructed a table with axes of m_l (-3 to +3 above) and m_s. Then hunds rules...
  17. W

    The ground state of a time-reversal invariant system must has zero momentum?

    if the ground state is non-degenearate, this is easily understood But what if the ground state is non-degenerate?
  18. R

    Why Would a Finite Well Fluctuate?

    If you make the length of a finite well shorter, then the energy levels should increase, because for example the uncertainty principle. But can the ground state, when squeezed, have such high energy that the energy is greater than the potential of the well? Does that even make sense?
  19. D

    Excited vs. Ground state masses of atom

    1. In a certain gamma decay process, an excited neon atom emits a gamma-ray that has an energy of 1.630 MeV. The neon atom in the ground state has a mass of 19.992 435 u. What is the mass of the excited neon atom? 2. I am pretty lost here. There must be a formula relating these...
  20. J

    Energy width of ground state neutral pion

    Homework Statement Most of the particles known in physics are unstable. For example, the lifetime of the neutral pion, \pi^{0}, is about 1.0 x 10^{-16} s. Its mass is 1.35 x 10^{8} \frac{eV}{c^{2}}. What is the energy width of the \pi^{0} in its ground state.Homework Equations \Delta E\Delta...
  21. N

    Wave mechanics: the ground state and excited state of nitrogen attom

    Homework Statement a) To get a wave function for a situation in which the energy is close to E_0 and the atom is almost certainly in one of the minama of the potential energy , consider the functions \varphi_t(x)=[(\varphi_0(x)+\varphi_1(x))/(2^(1/2)))...
  22. B

    Calculating binding energies of ground state electrons

    Homework Statement What is the calculated binding energy of the electron in the ground state of (a) deuterium, (b) He^{+} and (c) Be^{+++}? Homework Equations For the hydrogen atom, E_{n} = - E_{o} / n^{2} E_{o} = me^{4} / 2hbar^2(4\piEo)^2 The Attempt at a Solution Not sure...
  23. M

    Hydrogenic Atom emitting electron - probability of remaining in ground state

    Homework Statement Hi all - I've done all but the last part of this problem, for which I have the solution, but I was hoping someone could explain why the solution is what it is :) q:The Hamiltonian of a quantum system suddenly changes by a finite amount. Show that the wavefunction must...
  24. W

    Why lanczos algorithm is useful for finding the ground state energy?

    i am now reading some materials on lanczos algorithm, one of the ten most important numerical algorithms in the 20th century my puzzle is, why it is useful for finding out the ground state energy? i can not see anything special about the ground state energy in the algorithm
  25. W

    Electric dipole transition between hyperfine levels of the ground state

    microwave can be used to engineering potentials for alkali atoms i find that in the literature, people only take the magnetic dipole transition into account why the electric dipole transition is neglected? is it forbidden?
  26. K

    Can a ground state energy be negative?

    Just a short question. I have five energies. -25 eV -5 eV 0 eV 5 eV 25 eV The textbook definition is that the ground state is the state with the lowest energy, i.e. I believe 0 in this case. But that is taking the absolute value of theenergies. In reality the lowest energy is...
  27. T

    Why do electrons in excited states decay to the ground state?

    Hello, Non-relativistic quantum mechanics doesn't explain why the electron in the hydrogen atom (for example) "decays" from excited states to the ground state. Which theory does explain this phenomenon (from basic principles) ? Thanks.
  28. W

    What Is the Correct Ground State Energy of a Neutron in a Box?

    Homework Statement The particle in a box model is often used to make rough estimates of ground state energies. Suppose that you have a neutron confined to a one-dimensional box of length equal say 1 x 10^-14m. What is the ground state energy of the confined neutron? answer in MeV...
  29. K

    What is the Ground State Wave Function for an Electron in a 1D Potential?

    Homework Statement an electron moves in 1D and is confined to the right half (x>0) potential: V(x) = -(e^2)/(8piEx) E is the permittivity of free space the ground state wave function is Nxe^(-ax) N is normalization constant, and a is another constant needed to be determined Homework...
  30. O

    Is the ground state of a negative potential always even?

    Is the ground state of any negative potential that goes to zero at + or - infinity always even?
  31. E

    Estimating Ground State Energy Correction of Hydrogenic Atom

    Homework Statement using first-order perturbation theory ,estimate the correction to the ground state energy of a hydrogenic atom due to the finite size of the nucleus, assume it's spherical nucleus. Homework Equations you can employ the fact that the electrostatic potential fi...
  32. N

    Magnetic flux quanta in ground state hydrogen

    How many magnetic flux quanta exist within the ground state hydrogen atom? Thanks in advance.
  33. X

    Hydrogen atom ground state with zero orbital angular moment question.

    Hi all: As we know, if we solve the schrodinger equation, the ground state wavefunction is independent of theta and psi. We find the expectation value of ground state orbital angular momentum is zero. But if we don't do any mathematical calculation, can we conlude that? For example, Due to...
  34. K

    How Does a Delta Potential Affect Bound States in a Quantum Infinite Well?

    In QM, sometimes we will combine the delta potential and other familiar potential (like infinite potential well). And I am quite confuse with the bound state. For example, consider a 1D infinite potential well with width a and locate b/w [-a/2, a/2]. Now if we add in a delta potential...
  35. K

    Can I Tell if a State is Ground State?

    If I know the explicit form of potential, the energy and a specific eigenstate, but I don't know the general form of eigenstates and eigenvalues, can I tell if the state is ground state or not?
  36. N

    Ground State Energy: What Regulates & Why is it Constant?

    What regulates the ground state energy of a hydrogen atom? Why is it constant (more or less)?
  37. P

    Calculating Ground State Energy for Triple Ionized Beryllium

    Homework Statement Calculate the energy of the electron in the ground state of triple ionized beryllium, which has an atomic number Z = 4. Homework Equations -Z2 (13.6) N2 The Attempt at a Solution Z=4 as given and it is tripled so our N=3. We throw our numbers in...
  38. J

    Consider a Hydrogen atom in the ground state

    Homework Statement Consider a Hydrogen atom in the ground state Find: A- The Kinetic Energy, in eV B - The Potential Energy, in eV C - The Total Energy, in eV D - minimum energy required to remove the electron completely from the atom, in eV E - What wavelength does a photon with the...
  39. N

    ChEM: ground state eltron configuration

    Homework Statement Al3+ N3- Li+ Au+ Sr2+ Mn2+ Tl+ Br - Homework Equations The Attempt at a Solution no clue, the positives and negatives are messing me up
  40. J

    What Are the Ground and Excited State Energies of the He+ Ion?

    Homework Statement What are the energies of the ground state and the first two excited states of the He+ ion? Homework Equations En= - Eo/n2 The Attempt at a Solution n=1 for this problem (since there is only 1 electron) so the ground state would have the electron...
  41. S

    Ground state energy in Optical Spectroscopy & Atomic Structure

    Homework Statement I just want to know if there is a relationship between the ground state of Hydrogen which is 13.6 eV and the ground state of Helium. The problem is asking me to find the ground state of Helium, but I am not sure how to go about it. Any advice? Homework Equations...
  42. M

    Ground state of Hamiltonian describing fermions

    Homework Statement I have been given the Hamiltonian H = \sum_{k} (\epsilon_k - \mu) c^{\dag} c_k where c_k and c^{\dag}_k are fermion annihilation and creation operators respectively. I need to calculate the ground state, the energy of the ground state E_0 and the derivative...
  43. 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...
  44. S

    Ground state of 7 electrons in infinite square well

    Homework Statement Seven electrons are trapped in a one dimensional infinite square well of length L. What is the ground state energy of this system as a multiple of h2 / 8mL2?Homework Equations Energy of a single electron in state n is n2h2 / 8mL2The Attempt at a Solution Pauli exclusion...
  45. 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...
  46. L

    Perturbed Ground State Wavefunction with Parity

    [SOLVED] Perturbed Ground State Wavefunction with Parity Homework Statement A particle is in a Coulomb potential H_{0}=\frac{|p|^{2}}{2m} - \frac{e^{2}}{|r|} When a perturbation V (which does not involve spin) is added, the ground state of H_{0} + V may be written |\Psi_{0}\rangle =...
  47. michael879

    Is Annihilation Really Just Positronium Ground State?

    so I had this thought earlier today. I am not claiming this is true or even likely but its interesting, possible (from everything I know), and may be testable by experiment. What if annihilation doesn't actually exist? What if what we see as an electron annihilating with a positron is...
  48. H

    7th grade Ground State Harmonic Oscillator problem

    Homework Statement Calculate the probability for finding the ground state harmonic oscillator beyond its classical turning points. Homework Equations Psi n(q) = (alpha/pi)^(1/4) exp(−alpha*q^(2)/2), where alpha = (kμ)^(1/2)/h bar The Attempt at a Solution i know it's going to be...
  49. 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...
  50. 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...
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