Recent content by captainjack2000

Homework Statement Considering only orbital angular momentum, estimate the energy level separation between electron states in a magnetic field of 1 Tesla applied along the z direction. Homework Equations I am confused by how to even start this question! Isn't orbital angular momentum...

to be of unit length...which these are right?

are these normalised?

Thank you very much. So what I have done is for eigenvalue h+g I have two equations hx+gy=hx+gx and gx+hy = hy+gy which gives x=y so eigenvalue h+g has eigenvector (1,1) and for eigenvalue h-g I have two equations hx+gy=hx-gx and hx+gy=hy-gy so x=-y so eigenvalue h-g has eigenvector...

Homework Statement I have a matrix H= [h g g h] and I need to find the eigenvalues and normalised eigenvectors Homework Equations The Attempt at a Solution I subtracted lamda from the diagonal and then solved for the determinant equally zero. The eigenvalues I found were...

May I ask why you do not need to use the L^2 operator explicitly? How do you end up with your sum(an* am <En|H|Em>) term?

you first need to find the cut off frequency wd by using the linear dispersion relation. For the Debye model w is proportional to k. At the long wavelength limit k=pi/a where a is the dimension of the unit cell. Having found w you can then substitute it back into your first equation for temperature.

Does that mean that my wavefunctions look correct? How would they differ for the two lowest energy states?

Wavefunctions for Indistinguishable and Distinguishable particles - URGENT Homework Statement A one-dimensional potential well has a set of single-particle energy eigenstates Un(x) with energies En=E_o n^2 where n=1,2,3... Two particles are placed in the well with three possible sets of...

So how would you calculate the other eigenvectors. Sorry I am still confused.

Homework Statement The Hamiltonian of a system has the matrix representation H=Vo*(1-e , 0 , 0 0 , 1 , e 0 , e , 2) Write down the eigenvalues and eigenvectors of the unperturbed Hamiltonian (e=0) Homework Equations when unperturbed the Hamiltonian will...

Homework Statement I was trying to work through some quantum physics questions and I was getting a bit confused. I know that for fermions the wavefunction must consist of spin and spatial parts of the fermionic wavefunction with opposite exchange symmetry (ie antisymmetric spin and symmetric...

Homework Statement I am looking at the relativistic correction to the kinetic energy for a hydrogen atom. I am told that the perturbation is usually written as H = -p^4/(8 m^3 c^2) and need to find the energy shift Homework Equations I know that from the perturbation theory the energy...

Double Pendulum URGENT! Homework Statement I am trying to solve this past paper question for my exam tomorrow: A double pendulum is constructed using a light rod and light inextensible strings. Two string pendulums hanging from ceiling 1m long. 0.1m from top they are connected by a light...

Homework Statement Water is falling gently into a large tank at 0.2m^3s^-1 and leaves through a small hole in the bottom of the tank of area 0.05m^2. What is the water velocity as it leaves? How full is the tank in the steady state? Homework Equations Well if the rate of water...