Recent content by joelperr

It has been proven that non-standard analysis is equivalent to the 'normal' formulation of real analysis (i.e. the epsilon-delta formalism). Thus, since the two formulations are in bijection, 'proving' that classical mechanics and statistical physics work using axiomatic non-standard analysis...

http://en.wikipedia.org/wiki/Smooth_infinitesimal_analysis http://en.wikipedia.org/wiki/Nonstandard_analysis

The simple answer is that in standard formulation of general relativity, we require a unique connection on a manifold which is torsion-free and metric compatible, which lead to the properties of the covariant derivative that we need.

You don't get gravitons out of Einstein's field equations; those only show up when you attempt to generate an effective quantum field theory that includes gravity. For gravitational waves, the easiest method would be to use the weak-field equations in the transverse gauge, and set the...

A Hamiltonian is considered to be rotationally invariant if, after a rotation, the system still obeys Schrödinger's equation. Equivalently, you may show that [U,H] = 0 , which should be rather easy since your Hamiltonian is time-independent.

Matlab could do it, but it's not free; SciLab is a pretty good clone of Matlab, and it's available for all major platforms. However, if you're asking which software could do this kind of numerical analysis, then I assume that you are not familiar with either of the products that I've...

The best way to proceed is to write down the relevant equations for the conservation of momentum and conservation of energy: E_{1} + E_{2} = E_{final} \textbf{p}_{1} + 0 = \textbf{p}_{final} Initially, the first particle has kinetic and rest mass energy, and the second particle has only...

In general, the subscripts denote which parameters are held constant.

Show us what you have so far, and we can go from there. That might be one of the equations that will be used, but you need to show some sort of attempt at a solution instead of simply stating that you're getting an incorrect answer.

Given your choices to go into condensed matter physics and biophysics, I would say that this following order would be best: 3, 4, 1, 2. Biophysics sometimes has to deal a lot with bioinformatics, where #4 will come in quite handy. #3 is essential to any physicist, but especially in biophysics...

If this is your undergraduate, then neither will be appreciably different. Go to the one that is closer/cheaper (yeah, right).

Well, that depends on several factors; in the end you will just have to judge for yourself. However, I can tell you that the joint Honours programme in physics and mathematics here at my university boils down to pretty much that: either 3 physics + 2 math or 3 math + 2 physics for every...

Hook it up to the OSG (Open Science Grid) which will be doing computations for the LHC (Large Hadron Collider) when it comes online in 2007. That's the best use of resources I can think of.

Those are pretty standard classes for an intro physics programme; if you're motivated, it shouldn't be a problem.

Algebra by far. Group theory is the foundation of so many interesting and beautiful parts of mathematics; plus, as mentioned before, it will help you more on the GREs.