Seasons

PS yeah, I need help. At least I'm not hitting on a toaster.

Prob123, did you use really fine print or did my expression of intellectual self gratification make me go a little blind?

Oooh! Now, This site has really cool graphics! (Did I use "cool" correctly?)

http://www.colorado.edu/physics/2000/schroedinger/index.html

Bev, message 3947:

[blush] Well, er, {blush!] er, ah, well, maybe {BLUSH] once or twice, with a book I REALLY LIKED!!!!!

Bev 3947:

spurts??? What gender do you think I am?

I like the multiple solutions idea, though!

Prob123 3948:

I like the idea of bringing chocolate into it!!!

Chocolate covered quantum physics? I'd bite tthe ears off that bunny.

Schroedinger's bunny. Half of it melts in your mouth!

The interesting question is where was the chocolate before it melted? Not in your hands.

Psimagus:

Are we embarrassing you with all this girl talk? We may be talking about waves, but at least we're not discussing periods!

You wrote:

But how do you view the eigenvalues? Are they anything more than a mathematical device to explain what we observe, or do you see them as describing something that is causally "real"?

Well, technically, an eigenvalue is just a number. But an eigenvalue associated with an operator associated with a physical quantity in QM - that eigenvalue also has physical significance. For example, for a pointlike particle, the eigenvalues of the position operator are all the positions that the particle can have (actually, since space is three-dimensional, it takes three eigenvalues, one for each co-ordinate). A simpler example is spin, which in certain situations can have only one of only two values, "up" and "down." So Psi gives a probability that the spin is "up" and the probability that the spin is "down". Such claims can be empirically tested by repeating the experiment many times, measuring the spin each time. If the probability of spin "up" is 2/5, then in the long run the measurement should yield "up" about 2/5 of the time (and hence "down" about 3/5 of the time).

Now, in the case of the two-slit experiment, as discussed on the various sites mentioned above, the interference pattern gives the probability: where the interference pattern is "strong", the probability that an M&M will hit there is high. Similarly with my "spit bullet" example of several days ago.

"eigenvalue" is a very impresive word (people about to mug me have been known to bow down to me when I utter it), but all it really means is a possible value for a certain physical parameter of a system. For example, the momentum eigenvalues of a system are just the values of momentum that the system might have.