Recent content by TimH

Okay, my text says "If F,G share a complete set of eigenstates, then [F,G] vanishes," where "complete set" means a set of vectors that are linearly independent and span the space (i.e. a basis). I thought that since observables are Hermitian and therefore have a complete set, there was just one...

Okay, thank you for that. I wondered if [B,C] not equaling zero made it a straight 50-50 coin flip or not. Now I'm definitely a beginner at QM, I'm trying to get the overall structure (I'm reading a good text, Essential Quantum Mechanics by Bowman). So in the above situation A's eigenstates...

I'm teaching myself QM and have a question about a problem in my text. (If this makes it homework, sorry to post in the wrong forum). Basically the question is about three observables A,B,C. They obey the following rules: [A,B]=0, [A,C]=0, but [B,C] not equal to 0. So this is like the...

Thanks Hamster. I figured there was some general form. I'll play around with that.

Okay, I figured out what happened. Thank you for your posts. I first tried (1,0) and (0,i) on my TI-89 calculator, using the "completeness relation," i.e. that the ket-bra |x><x| of the two vectors, when added together, should give the identity matrix. It didn't work on the calculator which...

I'm teaching myself quantum mechanics and am learning about bra-ket notation. There is a particular operator used, the ket-bra (e.g. |X><X|). To understand it, I'm trying to come up with an orthonormal basis for C^2 as a simple case (i.e., the 2-dimensional vector space over the field of complex...

Thanks for the post, SpectralCat. This description is the kind of thing I was looking for and definitely helps. I'll take the basis-conversion formula in my book and try some conversions in real 2-and 3-d space between simple bases to see what you're describing. Its like...I know QM math is...

I know that if we take a real (i.e. non-complex) set of basis vectors, e.g. (1,0,0), (0,1,0), and (0,0,1) in the 3-dimensional case, and treat the column vectors of these as kets and row-vectors of these as bras (since the conjugate is the same value), then we get three 3x3 matricies that are...

I'm teaching myself QM using Zettili's book. I'v been chugging along seeing how linear algebra works in infinite-dimensional Hilbert space. Now the author has introduced the "completeness relation," that for an infinite set of orthonormal kets |Xn> forming a basis, Sigma(n=1 to infinity) of...

Okay I think I get it. The integral is of i*(sin(a)*sin(ax))/a. We're integrating wrt a. Now sin(a)/a is even. But sin(ax) is odd if we're integrating wrt a. So its an even function times an odd function which gives an odd, and so its integral is zero over the symmetric interval. And so...

I'm teaching myself some basic Fourier analysis from Boas's "Mathematical Methods in the Physical Sciences." I'm a little stuck on Example Problem 1 on p.382. This is a basic example of getting the g(a) Fourier transform of a certain function (pictured on the page) and then plugging it into...

Thanks for all your replies. The point (above) that the weight isn't really a factor definitely helps clarify things. Yes, I'm doing a Savonius design. I don't want to decapitate anybody on the lawn with long blades, and I want something compact I can move easily. So I'm thinking two thin...

I'm thinking of building a small vertical-axis wind turbine as a project over school vacation. By small I mean maybe three feet across and three or four feet high. I'm trying to come up with the best design. This type of turbine is good at generating torque, not RPM's, so I want to try to...

Jesse, Its been four months, which is too long, but I just came across your last post and want to thank you for taking the time to write it. It definitely helps.

Clever! I like it. The problem says as a hint not to use torque, which is why I went the way I did. Is there a way to get the answer with my approach? What I mean is, from ar, without using torque?