Physics Help Forum Trying to work with Susskind's Theoretical Minimum book

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 Dec 23rd 2018, 01:11 AM #1 Senior Member   Join Date: Nov 2013 Location: New Zealand Posts: 550 Trying to work with Susskind's Theoretical Minimum book Trying to figure out the above question. Susskind states the relationship between certain state vectors when using a measuring apparatus to detect spins in certain directions. He comes up with: $\displaystyle |r> = \frac{1}{\sqrt{2}} |u> + \frac{1}{\sqrt{2}} |d>$ and $\displaystyle |l> = \frac{1}{\sqrt{2}} |u> - \frac{1}{\sqrt{2}} |d>$ where u,o, l, r, i, o stand for the state vectors up |u>, down |d>, left |l>, right |r>, in |i> and out |o>. He also states the following experimental results = 0 = 0 = 0 = 0 = 0 = 0 and if it's an inner product with itself it equals 1 ( = 1, = 1, etc) and other combinations comes out to 1/2 = 1/2 = 1/2 = 1/2 = 1/2 et With respect to the first exercise I figured out the first part. It was merely taking the inner product and and same for and where u,o, l, r, i, o stand for the state vectors up, down, left, right, in and out. It gives me the info that = = = 0 and most of the other combinations = 1/2 when multiplied by their complex conjugate. But I am at a loss to know where to begin to derive $\displaystyle \alpha \beta^* + \alpha^* \beta$. I can't fathom how the alpha and beta symbols got transposed if we're limiting ourselves to inner products. Any advice? __________________ Burn those raisin muffins. Burn 'em all I say. Last edited by kiwiheretic; Dec 23rd 2018 at 10:33 AM. Reason: Clarifying.

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