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Inner products of vectors in the form of equations.

  1. Dec 29, 2015 #1
    I am in the process of reading through The Theoretical Minimum. One of the processes it suggests is relating to orthogonal vectors, particularly representing the right (|R>) and left (|L>) spins. Common sense says they're orthogonal but I was wondering how exactly to represent the inner product.

    for |R> they gave the equation |R>=(1/sqrt(2))|U> +(1/sqrt(2))|D> where |U> and |D> represent up and down spins respectively.

    for |L> they gave the equation |L>=(1/sqrt(2))|U> -(1/sqrt(2))|D> where |U> and |D> represent the up and down states.

    My first intuition was to put them in vectors in order to find <R|L>. I used the coefficients to find the different parts of the vector. It came out correctly but I wanted to make sure I was using the correct process.
  2. jcsd
  3. Dec 29, 2015 #2

    Simon Bridge

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    Welcome to PF;
    Yes - that is the correct process ... in general, you just apply the definition.
    Note: The equations you were given are also vectors.
  4. Dec 29, 2015 #3
    Thank you!
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