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    Helping students transition from High School to University

    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...
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    Snell's law question with a twist...

    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...
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    Muonic hydrogen, change in potential of the muon.

    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...
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    * * (Exam tomorrow morning!)

    *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...
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    Pauli spin matrices, operating on |+> with Sx

    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...
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    Eigenvalues of a matrix B= f(A) given eigenvalues of A

    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...
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    Deriving an expression for internal energy.

    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...
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    Complex functions, (z+i)^5 + (z-i)^5

    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...
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    QM- A Harmonic oscillator experiences an instantaneous change in it's spring constant

    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...
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    Looking for a solid Introductory Statisical Mechanics textbook.

    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...
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    QM- Probability of finding a system in a superposition of energy eigenstates.

    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...
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