Recent content by elemental09

Alright - thanks for clearing that up. I have always thought that, given the opportunity to study somewhere new, but with the cost of sacrificing the opportunity of working with someone better aligned to your interests, the latter should win out. I should have elaborated a bit more - from what...

Thanks for the reply, twofish-quant. I hear you with regard to finance. I will keep more of an open mind. To be honest, before I started in physics I toyed with the idea of being a trader, after doing a little temp work for a friend in that business. Some of what I saw was exciting, and I...

In a few months I should be graduating from the University of Toronto, having specialized in physics. Academically I have done well - my graduating GPA looks like it will be around 3.96 out of 4.00 (everything above 85%, except 84% in Linear Algebra II and 78% in Modern Optics). I have done...

Sorry it's taken me so long to reply to this. I still fail to understand why this is the case. I understand that time-dependent perturbation theory normally fails unless the transition probability being calculated is << 1, but I don't see why only one coefficient (I presume you mean only one...

Thanks for the reply. Indeed, the perturbation is implied to be small, so I guess it's reasonable to assume the perturbed, time-dependant eigenstates won't stray too far from their original form. Your next point is less clear to me. Why would only only one coefficient be appreciably...

Time-dependant perturbation theory & "transitions" I'm studying approximation methods, and something is really bothering me about the standard treatment of time-dependant perturbation theory. In lecture, the prof introduced time-dependant perturbation theory with the following motivation...

Entering my 4th year of physics at University of Toronto, the time has come to look at graduate school... I've just come across http://www3.imperial.ac.uk/theoreticalphysics/postgraduatestudy/mastersdegree", at Imperial College London, titled "MSc in Quantum Fields and Fundamental Forces". Its...

My proposal in post #1 was based on a flawed understanding of simultaneous eigenkets and compatible observables. I was operating under the idea that a simultaneous eigenket was one single ket, not the direct product of two subkets. In that case a measurement of A would collapse it to a single...

SpectraCat: there is a difference - were the first case true, every time one measures observable A of the system to be in a particular eigenstate, one can also immediately predict the outcome of B - namely, the eigenvalue of the simultaneous eigenket. However, I now see this is false, as...

Thanks for the reply. In this case, I need to clarify a point which was not made explicit in my course. I am aware that the total state vector describing a composite system, say two particles each with independent spins, consists of the direct product between two kets inhabiting two spaces, one...

I'm still learning the formalism and structure of standard QM, so bear with me. My current confusion arises when considering the subsequent measurement of two commuting observables, for example the x-position and y-position observables of a single particle. Suppose the system is in a pure state...

There could be several valence electrons, though. Though perhaps it is telling that Boyd uses this theory to calculate the third-order susceptibility third-harmonic generation in sodium vapour - sodium having one valence electron.

Sorry it took a while to respond. In fact before introducing any density matrices, Boyd still treats the atomic wavefunction as one-particle. In any case, I'll have to accept his treatment. But here's another question: the expressions obtained for the susceptibilites using this approach depend...

Thanks. That interpretation seems natural. But Boyd writes the atomic wavefunction for an arbitrary atom as being a function of only one spatial variable, and time, which agrees with what you have only for n=1. Similarly, expectation values are calculated as a single integral over all space, not...

I am participating in a reading course on nonlinear optics, which is a little difficult since I haven't had any formal education in quantum mechanics other than the standard introductory solving of Schroedinger's eqn. in 1D. Happily this course takes the semiclassical approach, in which the...