Inner products of vectors in the form of equations.

[SpartaBagelz]

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.

 

[Simon Bridge]

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.

 

[SpartaBagelz]

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!