Recent content by captainjack2000

1. Energy Level Separation

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...
2. Eigenvalues and Normalised Eigenvectors

to be of unit length...which these are right?
3. Eigenvalues and Normalised Eigenvectors

are these normalised?
4. Eigenvalues and Normalised Eigenvectors

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...
5. Eigenvalues and Normalised Eigenvectors

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...
6. Finding the expectation value of the angular momentum squared for a wave function

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?
7. Relationship between Debye Temperature and Speed of Sound in Metals

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.
8. Wavefunctions for Indistinguishable and Distinguishable particles -

Does that mean that my wavefunctions look correct? How would they differ for the two lowest energy states?
9. Wavefunctions for Indistinguishable and Distinguishable particles -

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...
10. Energy levels of helium atom

Homework Statement I have having difficulty explaining the splitting of helium atom energy levels for three different cases: 1)Coulomb interaction is ignored 2)Coulomb interaction is present but exchange interaction is neglected 3)Coulomb and exchange interactions are present The Attempt...
11. Structure factors

Homework Statement I have the ionic compound cesium chloride and have been asked to use the equation p(k) = (sum over j) exp(-iK.r)f(k) to find the structure factor for x-ray diffraction from cesium and explain why it can take two values. It also asks how you would expect the intensities...
12. Eigenvectors of the hamiltonian

So how would you calculate the other eigenvectors. Sorry I am still confused.
13. Eigenvectors of the hamiltonian

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...
14. Exchange interaction

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...
15. Energy shift using perturbation theory

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...