So this is my first quantum mechanics class and so far we have spent about a month (well 3 weeks) on just the mathematics.(adsbygoogle = window.adsbygoogle || []).push({});

So in my book, the author explores the ideas presented by the stern gerlach experiment. It related the beam of silver atoms traveling through the separators to light traveling through two crossed polarizes by making a parallel that even though you can eliminate the x component, it can be returned if the light goes though a medium that "rotates" the light. This made a lot of sense to me and I was very happy with the analogy. From this, they constructed the expressions for spin-1/2 eigenkets and operators.

So now the book is moving to the idea of deriving these expressions through the mathematics in quantum mechanics.

So first, since there are two even distribution after passing through a separator, thus from the probabilities you get.

[itex]|\left\langle +|S_x;+ \right\rangle |=|\left\langle -|S_x;+ \right\rangle| = \frac{1}{\sqrt{2}}[/itex]

Where [itex]|S_{x};+> [/itex] and [itex]|S_{x};- > [/itex] are the eigenkets for spin up and spin down.

This next step is where I am confused.

[itex]|S_x;+> =\frac{1}{\sqrt{2}}|+ > +\frac{1}{\sqrt{2}}e^{i \delta_1}|- >[/itex]

And then they say that the expression for the minus ket must be orthogonal since it is mutually exclusive and they get...

[itex]|S_x;->=\frac{1}{\sqrt{2}}|+>-\frac{1}{\sqrt{2}}e^{i \delta_1}|->[/itex]

This I think I DO get but why are they representing one term as a wave? This logical leap doesn't make sens to me. Is there some physical interpretation that would help me?

Thanks so much in advance for your help!

EDIT: The angled brackets were screwing up the Latex so I just used ">"

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# Need help understanding this: Deriving expressions for spin 1/2 systems

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