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...
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...
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.
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...
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...
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...
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...
Thanks
So
R=l * rho /A
where l is the length of the conductor
rho is the electrical resistivity of the material
A is the cross-sectional area of the conductor
So V=IR
I(1) = V/R(1) and I(2)=V/R(2) where I(1) is the inital current
taking a ratio
I(1)/I(2) = [V/R(1)]/[V/R(2)] =...
Homework Statement
A light bulb has a straight metal wire filament of 50 micro metres diameter and 10mm long and when powered with a 5V constant voltage supply it draws 0.5A of current. What happens to the current if the filament is replaced with one of three times the diameter?
Homework...
I follow that really well. Thanks.
I get that the mass gains a height of h=4.32mm
When trying to draw the right angle triangle I get a bit confused. If the length of the hypotenuse is the length of the string. The angle at the top of the triangle is theta, the angle through which the mass...
Homework Statement
A mass of M=0.5kg is suspended from a fixed pivot by a thin rope of length l=120cm. The mass is struck by a bullet of mass m=10g with a speed of v=150m/s which embeds itself into the lead mass. What angle does the combined mass swing back to?
The Attempt at a Solution...
So the Boltzmann factor is
exp(-E/kT)=0.05
I still don't understand what you would take as the energy of the gas. It can't have a factor of kT because then the T would cancel......
Homework Statement
A gas of hydrogen atoms has a fraction of atoms found in the n=2 quantum state of 0.05. What is the temperature of the gas?
The Attempt at a Solution
I think the gas molecules have an energy E=5/2kT (rather than E=kT ?? because diatomic gases have 5 degrees of...
Homework Statement
Just a quick question: does a fully inflated tyre have the same mass as a tyre that is punctured or uninflated?
Homework Equations
The Attempt at a Solution
The one that is fully inflated will have a greater pressure but I am not sure what this will mean in...
Homework Statement
A train is travelling at 30m/s and decelerates and stops. During this process a passenger notices that a penduum is inclined by 10 degrees to the vertical. Estimate how far the train travels before coming to rest
Homework Equations
The Attempt at a Solution
I...
We are only given the separation distance of the red lights but I think it is assumed that we know the wavelength of the light and the angular resolution of the eye.
Since the angle is so small and sin(theta)=theta can it also be assumed that tan(theta)=theta? If so the vector triangle would...
Homework Statement
Two red lights are separated by 5cm, perpendicular to your line of sight. How far away from them are you if they can just be resolved with the naked eye?
Homework Equations
angular resolution =sin(theta)=1.22lambda / D
spatial resolution = 1.22(focal length * lambda)/D...
Homework Statement
a body has temperature 27C at twelve oclock. The room temperature is constant at 16C. Two hours later the body was found to have a temperature of 24C. The temperature of a normal human body is 37C.Using Newton's law of cooling estimate the time of death.
Homework...
Homework Statement
I have that the general solution of a function is
f(\rho,t)=\Sigmac(m)Jo(\alpha\rho\a) exp[-Dtm^2]
where c(m) are constants.
I need to find an expression for c(m) in terms of an integral
Homework Equations
Orthogonality relation given is
\intdx x...