I am in the rather unique and exciting position of being able to design an extension curriculum for some gifted Physics students who are in their final year of high school. The goal of the curriculum is to help prepare them for university physics with tools and ways of thinking, without just...
Homework Statement
https://gyazo.com/f8cf156e7bd2f2511e3fa859e3732fe6
Homework Equations
Snell's law.
The Attempt at a Solution
I'm mostly confused about the relevance of the second medium (of index n2) given that the distance between the ring and the boundary is "small". Having attempted to...
Homework Statement
Taking the proton to be a uniformly charged sphere of radius 1 fm, ﬁnd an
expression for the change in potential experienced by the muon as compared with that
in the case of a point-like proton. Use ﬁrst order perturbation theory to calculate the
ground-state energy...
*URGENT* (Exam tomorrow morning!) Calculating a real integral using residue theorem
Homework Statement
See attached picture
http://imageshack.us/photo/my-images/827/unledozs.jpg/
Homework Equations
The Attempt at a Solution
Parts a) and b) are straightforward.
For b) I end up...
Homework Statement
What is the result of operating on the state |+> with the operator Sx?
here, |+> denotes the eigenstate of Sz with eigenvalue 1/2. I am working in units where h-bar is 1 (for simplicity, and because I don't know how to type it)
Homework Equations
S_i = \frac{1}{2} σ_i...
Homework Statement
Find the eigenvalues/vectors of A. (I can do this bit :P, A is a 3x3 matrix)
What are the eigenvalues and eigenvectors of the matrix B = exp(3A) + 5I, where I is
the identity matrix?
Homework Equations
The Attempt at a Solution
I have (correctly) found that A...
Homework Statement
Show that the change in internal energy of a simple system between states (V1, T1)
and (V2, T2) is given by
∆U = \int^{T1}_{T2} C_v\ dT + \int^{V1}_{V2} T.\frac{\partial p}{\partial T}|_V - p \ dV
Homework Equations
dU=dQ-pdV
The Attempt at a Solution
As U is a function...
Homework Statement
solve
(z+i)^5 + (z-i)^5 = 0
Homework Equations
The Attempt at a Solution
I have found the five possible values for z by expanding the original expression into powers of z and i. The imaginary terms cancel exactly, leaving a cubic equation in z which is easily solvable...
Homework Statement
In the time interval (t + δt, t) the Hamiltonian H of some system varies in such a way that |H|ψi>| remains ﬁnite. Show that under these circumstances |ψi> is a continuous function of time.
A harmonic oscillator with frequency ω is in its ground state when the stiﬀness of...
Title says it all really, I'm a second year undergraduate from oxford, and currently the textbook i've been using for stat. mech. is "Concepts in Thermal Physics", which was wirtten by my lecturer. I'd like (ideally) something a bit longer to work through suring the holidays, that would provide...
Homework Statement
A system at time t = 0 is in the state |ψ> = a|E1> + b|E2>, where |E1> and |E2>
are (normalised) energy eigenstates with two different energies E1 and E2, and a, b
are real numbers. Write down the state |ψ, t> for the system at time t. What are the
probabilities at time t to...