Inner products of vectors in the form of equations.

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The discussion focuses on calculating the inner product of orthogonal vectors representing quantum states, specifically |R> and |L> spins as defined in "The Theoretical Minimum." The equations provided are |R>=(1/sqrt(2))|U> +(1/sqrt(2))|D> and |L>=(1/sqrt(2))|U> -(1/sqrt(2))|D>, where |U> and |D> denote up and down spins. The correct approach to finding the inner product involves applying the definition of inner products to these vector representations, confirming the validity of the method used by the participants.

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SpartaBagelz
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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.
 
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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.
 
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Simon Bridge said:
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.
Thank you!
 

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