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...
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...
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...
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...
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...
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...
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...
Homework Statement
I have the equation -(ck^2)U(k,t)=d^2/dt U(k,t). And I need to find the general solution.
Homework Equations
The Attempt at a Solution
I can rearrange this into the form d^2 U/dt^2 + (ck^2)U(k,t)=0 but I am not sure of the form of the solution to this equation...
Homework Statement
By using the substitution u=cosx obtain the value of the integral
\int\delta(cosx-1/2)dx between 0 and pi
Homework Equations
I have no idea how to go any further with this apart from substituting in for u!?
The Attempt at a Solution
Homework Statement
obtaining the fourier transform of the hat function
h(x) = 1 if modulus of x</= 1
=0 otherwise
Homework Equations
F(k)=1/sqrt(2*PI) *integral from -1 to 1 of exp(ikx)
The Attempt at a Solution
I've carried through the transform and got an answer of...
Homework Statement
How would you expect the intensities of the Bragg reflections in the x-ray diffraction patterns of cesium, cesium chloride and cesium iodide to compare? (The atomic numbers of cesium, chlorine and iodine are 55, 17 and 53 respectively_
Homework Equations
The...
Homework Statement
Sodium chloride has a face-centred cubic structure which can be regarded as a primitive cubic structure with a basis of sodium atoms at fractional coordinatese (0,0,0) (0.5,0.5,0) (0,0.5,0.5) and (0.5,0,0.5) and chlorine atoms at (0.5,0,0) (0,0.5,0) (0,0,0.5) and...
Homework Statement
If a and b are 4-vectors give the definition of the scalar product a.b and demonstrate its Lorentz invariance
Homework Equations
The Attempt at a Solution
So (with 4-vectors double underlined!)
a.b = a0b0-a1b1-a2b2-a3b3
a' = (a0*gamma - beta*gamma a1 ...
Homework Statement
I am aving a bit of trouble understanding how to show something is a 4 vector. For example K = (v/c, 1/lamdba, 0, 0 ) Show it is a 4-vector. I am not quite sure how to start this.
Similarly I have the amplitude of a wave in frame S described as A=cos[2PI(vt-x/lambda)] and...
Homework Statement
Show that the most probable energy minimises the Helmholtz free energy.
Homework Equations
F=E-TS(E) where S(E) is the entropy of te system of given energy E.
The Attempt at a Solution
Not sure how you would 'show' is ????
P(E) = 1/Z *weight funciton*exp(-beta E)
Homework Statement
Using a coordinate system in whic x and y are due east and nort of the city and z is the radial distance outwards from te centre of te earth, find the compnents of w the earth's angular velocity vector. You may assume that the latitude of the city is lamdba = 34degrees...
Homework Statement
"Two non-interacting particles are placed in a one-dimensional harmonic oscillator potential. What are the degeneracies of the two lowest energy states of the system if the particles are
a)identical spinless bosons
b)identical spin-1/2 fermions?
Homework Equations...
Homework Statement
"A thin conducting spherical shell of radius a carries a charge q. Concentric with this is another spherical shell of radius b>a carrying a net charge Q. Describe how the charge is distributed between the inner and outer surfaces of the shells. What is te capacitance of the...