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. A

    Fourier transform of the ground state hydrogen wave function

    Hi! 1. Homework Statement From the website http://www1.uprh.edu/rbaretti/MomentumspaceIntegration8feb2010.htm we can see the Fourier transform of the ground state hydrogenic wave function : Φ(p) = ∫ ∫ ∫ exp(-i p r) (Z3/π )1/2 exp(-Zr) sin(θ) dθ dφ r² dr (1.1) After intregation...
  2. ShayanJ

    A UV and IR modes in ground state

    I'm trying to understand chapter 19 of these lecture notes. But I have some difficulties with what the author explains: 1) In page 176, under equation 19.3 he says: This is weird. If we are considering a local QFT, then how can he say IR physics can cause non-locality? What is he talking...
  3. JulienB

    Stark effect: find ground state

    Homework Statement Hi everybody! I have a problem related to first-order perturbation theory, and I'm not sure I'm tackling the problem correctly. Here is the problem: Consider a hydrogen atom in an externally applied electric field ##\vec{F}##. Use first-order perturbation theory to find the...
  4. ikihi

    A hydrogen atom transitions from n= 5 state to the ground state

    Homework Statement A hydrogen atom transitions from ni= 5 state down to the ground state. a) What is the energy of photon emitted from the transition of the hydrogen atom? b) What is the ratio of the momentum of the emitted photon to the momentum of an electron which possesses the same kinetic...
  5. hilbert2

    A Overlap of Ground States in Quantum Field Theory

    I was reading Peskin&Schroeder's QFT book, and there was some discussion about how ##\left|0\right>##, the ground state of a free field and ##\left|\Omega \right>##, the ground state of an interacting field differ from each other, and they outlined how the latter can be obtained by propagating...
  6. astrocytosis

    Using Hund's rules to find ground state L, S, J

    Homework Statement Using Hund's rules, find the ground state L, S and J of the following atoms: (a) fluorine, (b) magnesium, and (c) titanium. Homework Equations J = L + S The Attempt at a Solution I'm having trouble understanding what L, S and J mean on a basic level. I read the textbook...
  7. ShayanJ

    A Ground state wave function from Euclidean path integral

    From the path integral approach, we know that ## \displaystyle \langle x,t|x_i,0\rangle \propto \int_{\xi(0)=x_i}^{\xi(t_f)=x} D\xi(t) \ e^{iS[\xi]}##. Now, using ## |x,t\rangle=e^{-iHt}|x,0\rangle ##, ## |y\rangle\equiv |y,0\rangle ## and ## \sum_b |\phi_b\rangle\langle \phi_b|=1 ## where ## \{...
  8. X

    Probability wave function is still in ground state after imparting momentum

    Homework Statement An interaction occurs so that an instantaneous force acts on a particle imparting a momentum ## p_{0} = \hbar k_{0}## to the ground state SHO wave function. Find the probability that the system is still in its ground state. Homework Equations ##\psi _{0} =\left(...
  9. Christofferk

    Kinetic energy of the hydrogen atom in its ground state

    I saw another post about this but i didn't quite find what i was looking for there so i thought i'd give it a go instead with a thread. Homework Statement Calculate the exact value of the kinetic energy of the hydrogen atom in its ground state. No more information is given, we are referred to...
  10. adamaero

    Ground state energy for exciton in Si

    Homework Statement Estimate the ground state energy (eV) for an exciton in Si. εSi = 12 ε = 1.0359×10−10 Effective masses me* = 0.26me mh* = 0.36me effective mass = 0.15me Values of h 6.626×10−34 J⋅s 4.136×10−15 eV⋅s Values of ħ Units 1.055×10−34 J⋅s 6.582×10−16 eV⋅s Homework Equations E1 =...
  11. T

    Do all electrons orbit in the ground state, when the band ga

    Do all electrons orbit in the ground state, when the band gap, is increased, or decreased, as atoms come together to form molecules.? Like in glass, transparent liquids, and plastics. As atoms come together to form glass, like silicon, sodium, and calcium. Do the electrons orbital permanently...
  12. S

    Change in ground state energy due to perturbation

    Homework Statement Consider a quantum particle of mass m in one dimension in an infinite potential well , i.e V(x) = 0 for -a/2 < x < a/2 , and V(x) =∞ for |x| ≥ a/2 . A small perturbation V'(x) =2ε|x|/a , is added. The change in the ground state energy to O(ε) is: Homework Equations The...
  13. F

    Effect of spins on hydrogen atom ground state energy

    What do you think about Feynman's description (http://feynmanlectures.caltech.edu/III_12.html#Ch12-S3) ? It seems to be inconsistent with hyperphysics (http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/h21.html).
  14. T

    Ground state energies and potential

    How to compare the ground state energies if diagrams containing x vs V are given. I saw a problem containing diagrams three potentials and they have asked to arrange them in order of their ground state energies. One was a potential well, and the other two had small perturbation in the middle...
  15. S

    Solving Erbium's Ground State w/ Hund's Rules

    I have the solution for this problem but don't understand it. 1. Homework Statement Use Hund's rules to calculate the ground state of erbium with electron configuration [Xe]4f126s2 Homework Equations Hunds Rules: 1. Maximise S (within Pauli) 2. Maximise L (within Pauli) 3. Min J (for...
  16. Z

    Hydrogen atom ground state wave function complex conjugate

    For hydrogen atom ground state we know φ=π-1/2a-3/2e-r/1 I want to know the complex conjugate of φ* ?
  17. Chip

    An operator acting on the translated ground state of an SHO

    I am trying to perform the operation a on a translated Gaussian, ie. the ground state of the simple harmonic oscillator (for which the ground state eigenfunction is e^-((x/xNot)^2). First, I was able to confirm just fine that a acting on phi-ground(x) = 0. But when translating by xNot, so a...
  18. upender singh

    Ground state energy eigenvalue of particle in 1D potential

    Homework Statement a particle of mass m moves in 1D potential V(x),which vanishes at infinity. Ground state eigenfunction is ψ(x) = A sech(λx), A and λ are constants. find the ground state energy eigenvalue of this system. ans: -ħ^2*λ^2/2m Homework Equations <H> =E, H = Hamiltonian. p=...
  19. T

    Average potential and kinetic energies for H ground state

    Homework Statement Calculate the average potential and kinetic energies for the electron in the ground state of hydrogen. Homework EquationsThe Attempt at a Solution I know that KE = E - <U(r)>. I know that E = (-KZ^2e^2)/(2a0) and I know that U(r) = -KZe^2/r but I can't figure out how to...
  20. A

    Caculating ground state energy using GTO

    Using the single-electron wave function ψ(r) = N*exp( −ζr2 ) with ζ a variational parameter, how can we calculate the best approximation for the ground state energy of the hydrogen atom?
  21. Summer95

    Ground state wavelength and uncertainty Bohr/deBroglie model

    A check my work question... Homework Statement Louis de Broglie tried to explain Bohr’s hydrogen atom electron orbits as being circles of just the right circumference such that an electron of the Bohr energy going around the circle will interfere constructively with itself. This seems to...
  22. E

    Ground state and stationary states

    Can you please explain the difference between ground state and stationary state? In the stationary state, are the electrons at rest inside the atom?
  23. Tonia

    What is the max. # of electrons located in the ground state?

    < Mentor Note -- thread moved to HH from the technical chemistry forum, so no HH Template is shown > I need someone to check my answers and help me with the questions I couldn't answer. What is the max. # of electrons located in the groud state of a) an orbital 2 b) d sublevel 10 c) Be atom...
  24. C

    Ground state in an infinite square well with length doubling

    Homework Statement Assume a particle is in the ground state of an infinite square well of length L. If the walls of the well increase symmetrically such that the length of the well is now 2L WITHOUT disturbing the state of the system, what is the probability that a measurement would yield the...
  25. gfd43tg

    Expectation values r and x for electron in H2 ground state

    Homework Statement Homework Equations $$ \psi_{100} = \frac {1}{\sqrt{\pi a^{3}}} e^{-r/a} $$ The Attempt at a Solution a) $$\langle r \rangle = \frac {1}{\pi a^{3}} \int_0^{2 \pi} d \phi \int_{0}^\pi d \theta \int_0^{\infty} r^{3} e^{-2r/a} dr$$ This comes out to be ##\frac {3}{2}a##...
  26. L

    Translation operator on ground state

    Homework Statement I am working through a time independent perturbation problem and I am calculating the first order correction to the energy, and I am stuck operating the perturbation : v = i b (Exp[i g x]-Exp[-i g x]) on the ground state |0>. Homework Equations <0| v |0> = 1st order...
  27. R

    Saha equation partition function for Argon?

    This question is in regards to the degeneracy of states for an Argon atom with just one missing electron. For hydrogen the problem of finding the partition function depends on finding the the ionized state of hydrogen divided by the non-ionized state... (please see Saha equation ->...
  28. A

    Ground state energy for hydrogen-like “atom”

    Homework Statement For a hydrogen-like “atom” (e.g., He+ ion), with nuclear charge Ze, it is claimed that the the ground-state wavefunction is spherically symmetric and is given by ψ(r)=Aexp(−αr) , where A and α are constant. (a) Determine the normalization constant A in terms of α. (b)...
  29. naima

    Ground state of hamonic oscilator

    When i take a coherent state ##|\alpha>## if ##\alpha -> 0## then the limit is the Fock state for n = 0. so ##|n = 0> = |\alpha = 0>## The problem is that they seem to have different http://www.iqst.ca/quantech/wiggalery.php: Where is the error? Thanks. Edit sorry, in the link the W function is...
  30. binbagsss

    Momentum-Parity, ground state quantum no even-even odd-odd

    Notation: ##J^p## - ##J## the total angular momentum, ##p## the parity = ##+## or ## -. ## Ok so I'm given a diagram of energy levels, all have a ground state of ##0+##, except one which has a ground state of ##1+##. I'm askeed to indentify which set of energy levels belong to which nucleus...
  31. S

    The ground state e- is the largest negative value, but why?

    Hi Physics Forums! The ground state electron is the largest negative value, but what does this mean? Does this mean that kinetic energy is a positive value above zero? It seems at the ground state, the electron might also have kinetic energy as it is moving around as well as potential...
  32. N

    Energy Release of Electron Capture to Ground State

    Hello All, I am pretty sure that when a nucleus decays via e.c. and goes to the ground state all of the excess energy is released with the emission of the neutrino but was wondering if anyone could confirm/give a reference for this. Thanks!
  33. D

    Meaning of total ground state energy in periodic DFT calculations

    Dear all, periodic DFT codes (e.g. VASP) effectively simulate an infinite crystal due to the periodic boundary conditions. However, the energy value that one obtaines at the end of a simulation if finite. Frankly, I'm quite confused right now. Is the energy to be understood 'per unit cell'...
  34. R

    Ground state energy from the variational method

    Homework Statement Consider a one-dimentional particle in a box with infinite potential walls at x=0 and x=L. Employ the variational method with the trial wave function ΨT(x) = sin(ax+b) and variational parameters a,b>0 to estimate the ground state energy by minimising the expression E_{T}=...
  35. fluidistic

    Sudden perturbation, particle in a box, ground state

    Hi guys! Suppose there's a particle in a box, initially in its ground state. Suppose that one chooses a system of coordinates such that the potential V(x) is 0 from 0 to L. Suppose that one suddenly perturbate the system at a particular time so that V(x) becomes 0 from 0 to 2L. I've calculated...
  36. J

    Normalization of ground state "1/2hw"

    Hello everyone: I didn't have a complete view of the quantum field theory and cannot understand this question. We now there will always be fluctuation field in the universe which corresponds to the ground state energy 1/2hw of harmonic oscillator. In the free space, we will use box...
  37. A

    Probability of finding particle in shifted ground state

    Homework Statement At t<0 a particle is in the ground state of the potential V(x)= \frac{1}{2} mw^2x^2 . At t=0 the potential is suddenly displaced by an amount x0 to V(x)= \frac{1}{2} mw^2(x-x_0)^2 . a) What is the probability of the particle being in the ground state; the first excited...
  38. G

    Extracting ground state in path integral

    Suppose you have the transition amplitude in the presence of a source <q''t''|q't'>_{f} To extract the ground state, we change the Hamiltonian to H-i\epsilon , because we can write: $$|q't'>=e^{iHt'} |n><n|q> \rightarrow e^{iE_0t'} |0><0|q>=<0|q>e^{iHt'} |0>=<0|q> |0 t'> $$ where only...
  39. J

    Most probable electron location in Hydrogen ground state

    From the ground state wave equation the most probable outcome of anyone measurement will be in the center of the atom, at the nucleus. The expectation value is found to be the Bohr radius. So does this mean that if you measure the position of an electron in a hydrogen atom in the ground state...
  40. 2

    Deriving the ground state energy of a hydrogen atom?

    Homework Statement Hello! I am trying to derive the ground state enegry of a hydrogen atom, and have come to U=\frac{-mk_{0}^{2}Ze^{4}}{n^{2}\hbar^{2}} Problem is, I know there should e another factor of 2 in the denomenator because I get the ground state energy of hydrogen as being 27.145eV...
  41. A

    In ground state, are spins aligned or anti-aligned?

    In a past physics gre question (https://www.physicsforums.com/showthread.php?t=192334), we make use of the idea that the ground state energy of two ions that have spin is when the spins are aligned. However, the ground state of the helium atom is a spin singlet state, which is a linear combo...
  42. E

    The ground state of helium - showing that parhelium is ground state

    Homework Statement The Hamiltonian of helium can be expressed as the sum of two hydrogen Hamiltonians and that of the Coulomb interaction of two electrons. \hat H = \hat H_1 + \hat H_2 + \hat H_{1,2} The wave function for parahelium (spin = 0) is \psi(1,2) = \psi_S(r_1, r_2)\dot...
  43. C

    Ground state energy of harmonic oscillator

    Homework Statement 2N fermions of mass m are confined by the potential U(x)=1/2(k)(x2) (harmonic oscillator) What is the ground state energy of the system? Homework Equations V(x)=1/2m(ω2)(x2) The Attempt at a Solution I know the ground state energy of a simple harmonic...
  44. R

    Orbitals while transitioning from free electron to ground state

    I was thinking of putting together a visualization of electron orbitals as it transitions from unbounded or weakly bounded state to the ground state. However, it occurred to me that orbitals are symmetric about the proton. At some point the probability distribution must become asymmetric...
  45. C

    Ground state splitting due to spin interaction

    Homework Statement The interaction between the spins of the two particles in a hydrogenic atom can be described by the interaction Hamiltonian $$\hat{H_I} = A \hat{S_1} \cdot \hat{S_2}.$$ Compute the splitting of the ground state due to ##\hat{H_I}##. Both particles have spin 1/2. Homework...
  46. PsychonautQQ

    Ground State Energy of quantum oscillator

    My textbook says the ground state energy of the QSHO is given by 1/2*h_bar*w and that this is the minimum energy consistent with the uncertainty principle. However I am having trouble deriving this myself... ΔEΔt ≥ h_bar / 2.. so then ΔE/Δfrequency ≥ h_bar / 2... ΔE*2*pi / w ≥ h_bar / 2 ΔE ≥...
  47. C

    Radial distribution function for H atom in ground state

    Homework Statement The normalized energy eigenfunction of the ground state of the hydrogen atom is ##u_{100}(\underline{r}) = C \exp (-r/a_o)##, ##a_o## the Bohr radius. For this state calculate 1)##C## 2)The radial distribution function, the probability that the electron is within a...
  48. M

    Electron Excitation and Photon Emission: Understanding the Ground State

    Just curious: if an electron absorbs a photon of energy, it is in an excited state. The electron may go to a lower energy state (but NOT the ground state). Can a photon (of higher wavelength than absorbed) be emitted still? I don't quite see the importance of the electron having to go to the...
  49. T

    Estimate energy of infinite well (ground state)

    Homework Statement We have to estimate the ground state energy of an infinite potential well (1d) using an argument based on the Heisenberg uncertainty principal. We then are supposed to compare it with the exact value from the eigenvalue equation. Homework Equations Below The...
  50. A

    Ground state: singlet or triplet

    In my book it is mentioned that for the two 1s electrons the ground state is the singlet while for the two 2p electrons the ground state could be either singlet or triplet. Generally how can you determine whether the ground state is singlet or triplet?
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