Ground state Definition and 259 Threads

Homework Statement Already it is on title ! Homework Equations attachents provide the most relevant equations i could find. The Attempt at a Solution I have found some old books written in 1920 decade ,dealing with this subject,but the solution they provide seems very hard...

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 had a curious thought today, here is my logic: Charged particles have E fields. Moving charged particles create B fields. Electrons are moving charged particles, oscillating in an atom. Therefore, I concluded that an atom must be creating an oscillating EM wave, even in the ground state. But...

Hello again everyone! I would like to ask a question regarding this Hamiltonian that I encountered. The form is H = Aa^+a + B(a^+ + a). Then there is this question asking for the eigenvalues and ground state wavefunction in the coordinate basis. The only given conditions are, the commutator...

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...

Does anyone have the most up-to-date zero-point oscillation frequency for a hydrogen molecule? This is not a homework question, I'm thinking about incorporating it into a tattoo someday. I don't wish to have a tattoo with inaccurate info, so any help would be appreciated.

I noticed many PF threads mention ground state of Hydrogen atom. At the same time it is two body problem considered to be solved by separation of variables. It is true, of course, that we can find basis wave functions (solutions of Shroedinger equation). But why does anybody think, that...

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 Hey guys, I'm studying AS level physics at the moment in the UK and I'm having a hard time grasping the concept of the ground state of an atom, so my question is: Is the ground state the energy level that is closest to the atoms nucleus or is it the energy level that a...

Neon has lowest excited energy at 1(s^2)2(s^2)2(p^5)3(s^1) state. And the excitation energy is about 16.9eV. And next energy is at 1(s^2)2(s^2)2(p^5)3(p^1) state. And the excitation energy is about 19eV. In Franck Hertz experiment with Neon, current decrease at every 19eV, no 17eV. Why...

Homework Statement Folks, I am looking at a past exam question regarding the Harmonic Oscillator. The question ask 'Justify that the ground state of a harmonic oscillator a_\psi_0=0 equation 2.58 on page 45 of griffiths. THis was not covered in my notes. Any ideas how to justify this...

Hey all, I'm a student curently studying in a Singaporean Junior College (American 12th grade equivalent). I was curious and just thought of the following: Suppose a system with a electron and a proton nucleus, a hydrogen atom. From electrostatic force and circular motion equations- F =...

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...

Hi guys, Just got a question I'm a little stuck on and would love a push in the right direction Q) Using Hartree's theory calculate the degeneracy of the ground state of the Sodium atom. Its a previous exam question and I'm struggling to find much descriptive information about the topic...

Have to find the probability of measureing the ground-state energy of a particle. -in infinite potential well 0<x< a has wave-function \psi (x,0) = Ax(a-x) where a is the (known) length of the well, and the norm. const. A has already been found. The eigenvalues of the hamiltonian in...

I have confused myself with this by reading a combination of Wikipedia, books and my QM notes and I'm afraid I need someone to untangle me please. Basically what I want to know is, what are the consequences of the Pauli exclusion principle for the ground state of the helium atom? Here's my...

Homework Statement So to test the variational method of simple harmonic oscillator I am using some functions that can be a good approximations, such as: Gaussian: \psi(x)=Ae^{-bx^2} Polynomial: \psi(x)=1-bx^2+\frac{b^2 x^4}{2} (I just expanded the Gaussian into Taylor, I can use just...

uncertainty relation. I think I'm on the right track. Currently, I'm at, E = (1/2m)*<p^2> + (1/2)*k*<x^2> and when applying the uncertainty relation, deltax = <x^2>^(1/2) deltap = <p^2>^(1/2) How do I go about connecting everything from here? Thanks!

Homework Statement Verify that the ground state (n=0) wavefunction is an eigenstate of the harmonic oscillator Hamiltonian. Using the explicit wavefunction of the ground state to calculate the average potential energy <0|\hat{v}|0> and average kinetic energy <0|\hat{T}| 0> Homework...

Homework Statement A pion is a spin-0 particle with a negative unit charge. A neutron is a spin-1/2 particle with no charge. A proton is a spin-1/2 particle with positive unit charge. One can construct an unstable version of the hydrogen atom where the nucleus contains both a proton and a...

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...

Hi.. In a textbook, the ground-state wavefunction for any general Hamiltonian was under consideration. Then, a statement was made that this wave function is real since it is the ground state. Is it true that one can always choose the ground state wave function to be real? I understand...

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

Thanks in advance for anybody who is kind enough to help me. No this isn't for my homework. I am not even enrolled in school. I am doing some calculations for personal research. But I need to know the ground state radius of a muonic hydrogen atom to help prove my theory. I already know the...

Tha classical ground state is Ne\'{e}l state: every spin up is surrounded by nearest neighbours which are down, and vice versa. To give them a name, denote the spins down the A sublattice, and the spins up the B sublattice. Perform a canonical transformation on the B (but not on the A spins...

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

Must the ground state in an even potential of one dimension be the even parity?

The ground state electron configuration of Carbon atom is 1s^{2}2s^{2}2p^{2} For the electrons, 1s^{2}2s^{2}, L=0, S=0 So only consider electrons of 2p^{2}, and s_{1}=s_{2}=1/2 ---> S=0,1 l_{1}=l_{2}=1 ---> L=0,1,2 For S=0, L=0; J=0, so we have ^{1}S_{0} For S=0, L=1; J=1, so...

When given a Hamiltonian operator (in this case a 3x3 matrix), how do you go about find the ground state, when this operator is all that is given? By the SE when have H\Psi=E\Psi. I can easily solve for Eigenvalues/vectors, but which correspond to the ground state, or am I missing something?

Homework Statement Use leading order perturbation theory to calculate the ground state shift of hydrogen due to perturbation: \hat{V} Homework Equations 1. Leading terms in expansion of energy: E=mc^{2}+\frac{p^{2}}{2m}-\frac{p^{4}}{8m^{3}c^{2}}+... 2. \hat{H}=\hat{H}_{0}+\hat{V} where...

Homework Statement Find the ground state wave function for the 1-D particle in a box if V = 0 between x = -a/2 and x = a/2 and V = \infty Homework Equations I would guess -- Schrodinger's time-independent equation...

I'm not sure how to calculate the probability in a non-hydrogenlike atom. Perhaps I'm missing something. Z=1 to Z=2. Of course, n, the principal quantum number is n and l would be zero. http://i111.photobucket.com/albums/n149/camarolt4z28/2010-09-23195548.jpg?t=1285517610

I was reading Hasan & Kane's review on topological insulators and right in the beginning, page 3, they say that the Bloch ground state is U(N) invariant. I do not see that. Would anyone be able to show it or point to a reference? Thanks, Jan.

As I understand, it is postulated that only coherent states in LQG correspond to classical spacetimes. Is the ground state of LQG a coherent state? Otherwise, what principle selects that the universe should be in a coherent state?

Hello everyone, I want to know the presently existing works on the topic of ground state properties of Hubbard model (spin-1/2-, or extended- ). I am nonexpert and have not googled for useful information. Please tell me some articles or monographs on this if you know. Thanks!

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...

What does the Ground State of a quantum simple harmonic oscillator represent physically? Thanks in advance.

Ok so I've been wondering, how is it that physicist's EXPERIMENTALLY determine the ground state configuration of electrons in a particular atom? In other words do they use emission spectra/thermodynamic calculations/etc? Also, if ground state represents an atom's minimal energy state, which...

Homework Statement A particle is prepared in the state \psi (x) = \frac{1}{\sqrt{L}} in a region 0 < x < L between two hard walls (particle in a box). Calculate the probability that the particle is found in the ground state when its energy is measured. Homework Equations This question...

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...

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...

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...

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...

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...

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...

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

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

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...

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...

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...