Spin states. Notes from 3-11 added.

For the material we cover Tuesday (see the post below), spin will play a critical role. At the enclosed link is a summary of the states of two spins (of two electrons). Familiarity with these states, especially the spin state of two electrons:
\(\frac{1}{\sqrt{2}}(\uparrow \downarrow - \downarrow \uparrow)\)
 will help you follow our lecture/discussion on Tuesday.

https://drive.google.com/file/d/0B_GIlXrjJVn4a18zY3pscGZDRzg/edit?usp=sharing

Spin states play a huge role in quantum physics in general (and in quantum computing in particular). Here is the key thing: because electrons are Fermions, their overall state (spatial & spin) is required to be antisymmetric (with respect to the exchange of two electrons). When the spin state fulfills that requirement, the spatial state will be symmetric. When the spin state does not fulfill the anti-symmetry requirement then the spatial state must be anti-symmetric. This can make a big difference in the spatial state and thereby dramatically effect the nature and energy of the ground state.

With regard to quantum computing, for example, in a double-well-qubit the spins states:  \(\frac{1}{\sqrt{2}}(\uparrow \downarrow - \downarrow \uparrow)\) and \(\frac{1}{\sqrt{2}}(\uparrow \downarrow + \downarrow \uparrow)\) are regarded as the canonical "0" and "1" states of the qubit.

Please feel free to post questions and comments here.
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Added notes from Tuesday class, 3-11-14:

Also,
https://drive.google.com/file/d/0B_GIlXrjJVn4N3VkZ2dhYU00cWs/edit?usp=sharing