Ground state Definition and 275 Threads

when a continuous symmetry is broken, we say that the ground state is just one of the possible ground states, and there is no energy cost in moving from one to the other.. why doesn't the state keep changing with the slightest perturbation (production of goldstone boson). why don't we have a...

can "light" excite an electron from ground state to a higher state? An electron of a particular atom can absorb a discrete amount of energy, leap to a new quantum level, and then jump back down to lower states (emitting photons). My understanding is that going from n=2 to the ground state a...

Homework Statement How much energy (in kJ) does it require to remove an electron out of the ground state of hydrogen atom completely, according to Bohr? Homework Equations The Attempt at a Solution

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...

Hi, If I have the Hamiltonian: H=(1/2)p^2+(1/24)\lambda(x^2-v^2)^2 what is the best way to find the ground state wave functions \psi(x) . I was thinking this sort of looks like the harmonic osscilator, so maybe a clever change of variables could do the trick? or some form of perturbation...

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...

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...

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 (stable configuration at T = 0) of the one-dimensional ising model with first and second neighbour intercations: H = -J_1 \sum_{i} s_i s_{i+1} -J_2 \sum_{i} s_i s_{i+2} where s_i = \pm 1 The Attempt at a Solution I really don't know what i...

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...

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...

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...

Homework Statement Calculate the ground state magnetic moment of 7Li using the below equations. The spin value is 3/2. Homework Equations mu_J = gamma_J * J* hbar = g_J * u_N with g_J = [g_l + (g_s - g_l)/(2l + 1)] where g_l and g_s are orbital and intrinsic spin g factors for...

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...

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 =...

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...