Ground state energy Definition and 56 Threads

  1. 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...
  2. hilbert2

    A 2-electron system under compression

    I did some calculations for the ground state energy and wave function of a system of two electrons put in a finite-depth 2D potential well. Regardless of the shape of the potential well (square or circular), the expectation value of the electron-electron distance ##\langle r_{12}\rangle =...
  3. 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...
  4. Tanmoy

    Ground State Energy: Explanation & Calculation

  5. 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...
  6. 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...
  7. 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?
  8. 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?
  9. 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...
  10. 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...
  11. 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
  12. 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
  13. 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...
  14. 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...
  15. 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 =...
  16. 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...
  17. 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).
  18. E

    Ground-state energy of harmonic oscillator(operator method)

    I studied this from Griffith Chapter 2, with the algebraic (raising and lowering operator) method, we reached the ground state by setting a_Ψ0 = 0 , then we got what the ground state is, and then plugged it in the Schrodinger equation to know the energy, and it turned out to be 0.5 ħω. My...
  19. 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=...
  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. 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)...
  22. 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'...
  23. 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}=...
  24. 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...
  25. 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...
  26. 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 ≥...
  27. S

    Finding the ground state energy of a particle

    For a particle with a force acting on it whose potential is given by U(x) = g*lnx for x>1 and U(x) = ∞ for x = 1, how do I calculate the ground state energy of the particle? Supposedly, there is no need to use Schrodinger's equations for this question, which is why I have no idea how to start...
  28. J

    Perturbation Theory: Calculating for the correction on the ground state energy

    Homework Statement Homework Equations E_{1}=<ψ_{1}|V(r)|ψ_{1}> The Attempt at a Solution That is equal to the integral ∫ψVψd^3r So I'll just perform the integral, correct ? But r is not constant here right? So, I' ll keep it inside the integral? How should I continue? Please...
  29. 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...
  30. 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...
  31. 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...
  32. B

    What Is the Ground State Energy of a Particle in a Modified Potential Well?

    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...
  33. 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...
  34. 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...
  35. 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...
  36. 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...
  37. M

    Ground state energy of nucleus

    How do we compute the energy of the ground state using nuclear shell model?
  38. P

    Muonic hydrogen ground state energy

    Would the energy just be a multiple of how much bigger it is than electron?
  39. 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...
  40. 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 +...
  41. 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...
  42. 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
  43. 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...
  44. 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...
  45. 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...
  46. 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...
  47. 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...
  48. 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...
  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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