# Properties of Inner Product

1. Jul 24, 2014

### flydream19

Hey guys I'm new here and I've been using MathType for all on-screen math. For some reason PF doesn't recognize the built-in Dirac's bra-ket notation. (i.e. <$\psi$|) So I've included my equations and solution in the format of images, hopefully it isn't a problem.

1. The problem statement, all variables and given/known data
Proof that

2. Relevant equations
All other properties of inner product.

3. The attempt at a solution

#### Attached Files:

File size:
1.8 KB
Views:
121
• ###### Solution.gif
File size:
39.1 KB
Views:
152
2. Jul 24, 2014

### flydream19

Sorry I just realized a typo in my solution, but it doesn't affect the result:
The typo is at where I said: "Then I moved on to the right side:"
$$\alpha^*=6-5i$$
$$\beta=1+i$$
The beta should have a complex conjugate symbol (*):
$$\beta^*=1+i$$

3. Jul 26, 2014

### Redbelly98

Staff Emeritus
In your initial calculation of $< \alpha \omega |$, the middle term is wrong. I haven't checked over your math any further than that and the $< \beta \omega |$ calculation.

p.s. Moderator's note: I am moving this to Advanced Physics -- it doesn't really look like Introductory level physics to me, which we consider to be through (U.S.) college sophomore level.

p.p.s. In LaTeX, simply typing "<", "|", and ">" for bras and kets seems to work okay, but not great.

4. Jul 26, 2014

### collinsmark

As another $\LaTeX$ option is to use the /langle and /rangle together with "|" to do Dirac bra-ket notation.

For example,
Code (Text):
$$\langle x | y \rangle$$
yields
$$\langle x | y \rangle$$

[Edit: I still can't get them to scale up automatically though, in case the things in the bras and kets are larger and more complicated.]

Last edited: Jul 26, 2014