Ground state energy Definition and 60 Threads

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...

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 =...

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...

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...

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...

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?

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

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...

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...

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

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

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...

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...

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 =...

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...

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).

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...

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=...

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?

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)...

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'...

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}=...

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...

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...

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 ≥...

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...

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...

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...

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...

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...

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...

I'm asked to show that in the ground state, a particle trapped in a potential well approximately equal to its lowest allowed energy. I know the expression for the energy is h^2/8mL^2 for a finite well, and ΔEΔt~h/2π. But I'm at a loss as to how I'm supposed to even begin to start this...

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...

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...

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...

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...

1) The problem is about finding the ground state energy of electron in an infinite 2D circular and square potential well with the same area. I have calculate it via method of separation of variables in polar and cartesian coordinate respectively, and it is found out that the one on the circular...

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

Would the energy just be a multiple of how much bigger it is than electron?

Homework Statement An electron is confined to a potential well of finite depth and width, 10^-9 cm. The eigenstate of highest energy of this system corresponds to the value \xi = 3.2. a. How many bound states does this system have? b. Estimate the energy of the ground state with respect...

Hello everybody, I just have no idea how to start this problem so i was hoping you guys would point me in the right direction and then i'll be able to go on by myself the problem asks to show that the total ground state energy of N fermions in a three dimensional box is given by E total =...

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...

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 +...

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...

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

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...

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...

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...

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...