# 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...