Recent content by AlexChandler

If the OP was familiar with measure theory, I don't think the question would have been asked in the first place.

Can you reference the results you are talking about? They do not seem correct as stated... for example you can certainly take a definite integral of a step function, which has a discontinuity.

Also, a couple of comments are in order regarding your initial post. 1) It doesn't make sense to ask whether a function is measurable with respect to a sigma algebra. What you should be asking is how to show that the function f is measurable with respect to the measure space (which...

You need to show the function is measurable with respect to the lebesgue measure. Thus given \alpha \in \mathbb{R} you must show that \{x|f(x)< \alpha \} is a lebesgue measurable set.

Just as always, you must show that \{x : f(x)< \alpha \} is a set in the sigma algebra for any \alpha \in \mathbb{R}.

It is necessary for you to make some attempt at a solution. If you have not already done so, read a chapter in a classical mechanics book on central force motion. For example chp 8 in thornton and marion Classical Dynamics. The steps for solving such a problem will be outlined for you there.

The point is that they are exactly the same integrals. It doesn't matter if you use x or y or Ω or √ or ∏ to label the variable, it is simply the same integral. It is like asking if the solutions to the following equations will be the same or different: λ+2=1 θ+2=1 it doesn't matter...

Not sure exactly what you mean by that. However, what you should do is set up the integrals needed to calculate <x^2>,<y^2> and <z^2>. Look for similarities between the integrals. Do they look the same or different? For example: consider the following integrals, \int_0^5 (y+2)^2 dy and...

The term 'expectation value' is an unfortunate one and really should be something more like 'ensemble average'. Imagine you know all of the accessible quantum states of a given system, and there are g of them. And you were to construct an ensemble of g systems one in each of the accessible...

There is no angular dependence in the ground state. Then what can you say about the relation between <x^2> , <y^2> and <z^2> ?

I thought about it for a bit, read a bit on wikipedia and was going to summarize what I read, but i'll just give you the link. http://en.wikipedia.org/wiki/Measurement_in_quantum_mechanics I just think about it in the practical sense. A measurement is something you do in a lab with rulers and...

yes that is right, but the last part does not prove anything, only the first part is important

Actually I just bought this book. It is very good, however I feel it is a bit above my current level in my understanding of quantum mechanics.

The difference is certainly half odd integral, but not necessarily 1/2 :D And i believe the difference is that half integral spin particles permit spin multiplets with an even number of states, and integral spin particles permit spin multiplets with an odd number of states. Even and odd numbered...

Thanks so much for your reply! I don't really know anything about Lie algebra yet, but this definitely helps me understand a bit of what I need to learn in order to pursue the topic further. Could you possibly recommend a good book or books that I could buy that would cover these types of...