Ground state energy Definition and 56 Threads

Homework Statement V(x) = k|x|, x \in [-a,a], V(x) = \infty, x \notin [-a,a]. Evaluate the ground state energy using the variational method. Homework Equations a = \infty and \psi = \frac{A}{x^{2}+c^{2}}. The Attempt at a Solution 1 =...

I am looking at a diatomic molecule where the Hamiltonian is given as H = l²/2I + F*d*cos theta where d is the dipole moment. The term F*d*cos theta is small. I write the energy of ground state as E_0 = \hbar*l*(l+1)/ 2I Than I have to determine how much the ground-state energy...

Can someone explain to me why the ground state energy of a free electron fermi gas is not just: E = 2 \int_0^{k_f} \frac{\hbar^2 k^2}{2m} 3k^2 dk Where the factor of two is due to the fact that there are two electron states for each value of k. The idea is to add up all the energies of...

This is my second post concerning a question I had from Hawking book. I am completely new to this subject, and lack the mathematical background necessary to fully understand these concepts, but I hope that by posting my question I will at least not be so confused about it after receiving some...

What is the ground state energy of the following. (a) an electron Well the formula is: E_n = (h^2/(8*m*L^2))*n^2; The ground state means, n = 1, its the lowest enegery level possible. So i plugged in n = 1, mass of e = 9.11E-31; h = 4.136E-15 eVs; L = 100 pm, because the book says that's...

anyone happen to know how to estimate the ground state energy of a vee-box using the uncertainty principle?