Recent content by inquire4more

Right, qbert, I follow you. What I cannot understand is the point to conjugating the first equivalence so as to arrive at the second one. Doc Al typed what I arrived at when working over the proof, which very naturally seems more, well, natural. Is there some reason to go by way of the second...

You are absolutely right Mr. Grime, which is why I thought perhaps this question was better suited under a linear algebra thread. Line 2 is correct, as near as I can tell anyways, I just do not understand the reason for this particular form. Oh well, I'll just have to give it some thought.

Haha...thanks. I find it so interesting that line 2, though undoubtedly less natural, is in fact correct and can't help but wonder if Ballentine chose to state it in this form for some reason. Honestly, I can understand some minor typo passing the editor with greater ease than some quite true...

At the risk of arrousing the ire of the moderaters for posting the same topic in two forums, I again ask this question as no one in the quantum forum seems to be able to help. So... Regarding a proof of the orthogonality of eigenvectors corresponding to distinct eigenvalues of some Hermitian...

Right, no dispute there. I quite like the book. My issue is with the development of the proof. I am simply not grasping the development of the proof as concerns line 2 and was wondering if perhaps someone might shed some light on this for me.

Thank you. I arrived at precisely the same result, only arriving at the given line 2 by the conjugation and multiplication by -1. This is not my proof. It is one given in a textbook entitled Quantum Mechanics: A Modern Development authored by a Leslie Ballentine. I cannot determine why line...

I'm not sure if this is the appropriate section, perhaps my question is better suited for Linear Algebra. At any rate, here goes. Regarding a proof of the orthogonality of eigenvectors corresponding to distinct eigenvalues of some Hermitian operator A: Given A|\phi_1\rangle = a_1|\phi_1\rangle...

Now, there you have given me some food for thought which I will mull over for some while and if I come to some conclusion I will get back to you. Don't hold your breath. You are quite correct here. I simply enjoy the existence arguments and this thread seemed appropriate.

Wow, the exact problem I was having a couple of months or so ago... This might be of some help, maybe... https://www.physicsforums.com/showthread.php?t=94777

I see your point, but I contest it. Two piles of stones dumped all together does indeed make just a larger, singular, pile of stones. But these piles are not irreducible. And, in any course, we may say that we have created a pile with twice as many stones as either of the two earlier piles...

If that corner I'm in is an idea, then it was always there...:-p In all seriousness, I do not imply in any way that physical entities are any less real. I only state that some things, though not all, require a construction for their existence as such. A computer requires a construction of...

A computer is an entity, not an idea or truth. The truth of the statement 1+1=2 holds, ireespective. One object added to another object give us two such objects. We may have given names to the number, but we did not invent number, or truth.

I think your one assumption is enough, that is to say, assuming the universe is completely deterministic (I am not in fact asserting any of these things, simply following his argument) you must, in this case, enter the car. I think foreknowledge of the event would only affect the case in a...

Wouldn't that corpsy smell really get to you though? Sorry :frown: I feel kinda rotten now.

For what it's worth, and if anybody cares, I yesterday found my Munkres' topology text, and he had something interesting to say, somewhat justifying my initial dissatisfaction with the definition of the empty intersection. Regarding \cap_{A \in \alpha} A = X for \alpha = \emptyset, Munkres...