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

 Quantum Physics Quantum Physics Help Forum 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.  Tags book, minimum, susskind, theoretical, work Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post acarolina General Physics 5 Oct 8th 2018 01:38 PM p75213 Quantum Physics 2 Dec 26th 2010 11:38 AM becko Theoretical Physics 3 May 11th 2010 08:36 PM s3a Kinematics and Dynamics 1 Apr 18th 2009 09:34 PM 