Simple Dirac Notation Problem: Dot Product of Two Vectors

[Jalo]

Homework Statement

Imagine you have two vectors |a> and |b> such that:
|c> = |a> + |b>

Now imagine you want the dot product:

<c|a>

Is that the same as:

<c|a> = [ <a|*+<b|* ] |a> = <a*|a> + <b*|a>

where * represents the complex conjugate of the vector?

Homework Equations

The Attempt at a Solution

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Thanks in advance for any answer.

Daniel

 

[Simon Bridge]

You'd not normally put the star outside the bra like that.
if a is a state then |a> is the state vector corresponding to wavefunction Y_a ... we may sometimes write |Y_a> when you are starting out.

$<\psi_a|\psi>= \int \psi_a^\star \psi$

(I'm hoping someone else can do a better job of this explanation. :/ )
BTW: you know your vector |c> is not normalized right?

 

[Jalo]

You'd not normally put the star outside the bra like that.
if a is a state then |a> is the state vector corresponding to wavefunction Y_a ... we may sometimes write |Y_a> when you are starting out.

$<\psi_a|\psi>= \int \psi_a^\star \psi$

(I'm hoping someone else can do a better job of this explanation. :/ )
BTW: you know your vector |c> is not normalized right?

Yes, I'm aware that |c> is not normalized, but in this case it doesn't matter. I'm just learning the math behind Dirac's notation. I am not yet working with state vectors or anything of that kind.
Thanks for your answer!