## Thursday, February 23, 2012

### more homework hints

Wikipedia now has good introductions to specialized topics in physics and mathematics. You might enjoy the page on linear transformations. Or the one on eigenvectors.

## Wednesday, February 22, 2012

### homework hints

-- For problem 2, from Griffiths p. 441: "If you know what a particular linear transformation does to a set of basis vectors, you can easily figure out what it does to any vector." The trick is to work out how you would like a transformation to act on the basis vectors. You'll find (and you might check) that your result works for an arbitrary vector.

-- For problem 3: Based on what Griffiths has told you, you can work on the first two parts of the problem. As Donaldo pointed out to me in the reading questions, Griffiths and I haven't told you enough to understand equation A.75, which is important for the third part (the part about eigenvectors of L_x). Take a stab by guess-and-check, or we'll talk about it in class Friday.

-- For problem 3: Based on what Griffiths has told you, you can work on the first two parts of the problem. As Donaldo pointed out to me in the reading questions, Griffiths and I haven't told you enough to understand equation A.75, which is important for the third part (the part about eigenvectors of L_x). Take a stab by guess-and-check, or we'll talk about it in class Friday.

## Monday, February 20, 2012

### Quantum computing

*The Vancouver*

*Sun*reports from the annual meeting of the American Association for the Advancement of Science, held in Vancouver over the weekend, about the state-of-the-art in quantum computing.

Here's the basic idea behind it: Instead of representing the digital 1 and 0 of the computer by the "on" and "off" states of a transistor, you represent them by something like the two spin states of an electron, spin "up" and spin "down." As you know, the general state of an electron is a superposition of these two states. This would correspond to a superposition of a 1 and a 0. The computer could compute on both values at once. A string of 1s and 0s would be a series of electron spins, superpositions of 00010101, 00010111, 00010001..., an exponentially large number of possibilities going at the same time.

It's not often you come across a field at the cutting edge of experiment and theory, where the practical applications are within reach. The folks at D-Wave started selling some sort of primitive ($10,000,000) machine last year, to much controversy. You might enjoy Scott Aaronson's blog wrap on D-wave (dated by a few years). It's a window into the practice of science and the competing priorities of academic and industrial researchers.

Hopefully we can discuss quantum computing in more detail later, either online or in class toward the end of term. If I could choose my path in physics all over again...??

Oh, and the

*New York Times*reports yesterday on a transistor created from a single phosphorus atom.

### Midterm exam dates

The first midterm will be on Wednesday, March 7. The second midterm will be on Friday, March 30.

## Monday, February 13, 2012

### Textbooks in the library

This afternoon I added a copy of Griffiths to the copy of Feynman on course reserve. It may take 24 hours for it to hit the shelves.

### Quantum in the news: laser-entangled diamonds

We talked today about how an atom entering an open T apparatus will be in a superposition of the three T base states. We wrote: |S+> = c_+|T+> + c_0|T_0> + c_-|T_->. Those states, or the paths they represent, interfere with each other so that the atom leaves the apparatus in the same |S+> state.

It sometimes happens that two particles interact so as to enter a superposition in which the spin state of one depends on the spin state of the other. Neither is in a definite spin state by itself. These particles are said to be entangled, and they can remain entangled over long distances. (This has been tested for separations of many meters, but in principle there's no limit.) Griffiths pp. 421-422 discusses some of the "spooky" consequences of entanglement.

Recently researchers have been demonstrating entanglement in macroscopic (roughly, human-sized) systems. Usually on this scale the effects of entanglement are washed out by uncontrolled interactions with the environment. Here's an article describing a sweet experiment in which physicists, wielding lasers, managed to entangle two chips of diamond. The diamond chips were entangled for all of 350 femtoseconds. (That's 350 * 10^-15 seconds, for those counting.)

It sometimes happens that two particles interact so as to enter a superposition in which the spin state of one depends on the spin state of the other. Neither is in a definite spin state by itself. These particles are said to be entangled, and they can remain entangled over long distances. (This has been tested for separations of many meters, but in principle there's no limit.) Griffiths pp. 421-422 discusses some of the "spooky" consequences of entanglement.

Recently researchers have been demonstrating entanglement in macroscopic (roughly, human-sized) systems. Usually on this scale the effects of entanglement are washed out by uncontrolled interactions with the environment. Here's an article describing a sweet experiment in which physicists, wielding lasers, managed to entangle two chips of diamond. The diamond chips were entangled for all of 350 femtoseconds. (That's 350 * 10^-15 seconds, for those counting.)

## Sunday, February 12, 2012

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