Why Doesn't MathType Recognize Dirac's Bra-Ket Notation?

[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. <[itex]\psi[/itex]|) So I've included my equations and solution in the format of images, hopefully it isn't a problem.

Homework Statement

Proof that

Homework Equations

All other properties of inner product.

The Attempt at a Solution

 

[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:"
[tex]\alpha^*=6-5i
[/tex]
[tex]
\beta=1+i
[/tex]
The beta should have a complex conjugate symbol (*):
[tex]
\beta^*=1+i
[/tex]

 

[Redbelly98]

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

 

[collinsmark]

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

For example,

[tex] \langle x | y \rangle [/tex]

yields
[tex] \langle x | y \rangle [/tex]

[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.]

 

[paranormal]

Hi there! Welcome to the forum. I am a scientist and I would be happy to provide a response to your question about the properties of inner product.

First of all, I would like to commend you for using MathType to present your equations and solutions. It is a great tool for writing mathematical expressions and it is widely used in the scientific community.

Now, let's move on to the properties of inner product. The inner product is a mathematical operation that takes two vectors and produces a scalar value. It is commonly denoted by <x,y> or (x,y) and is defined as x1y1 + x2y2 + ... + xnyn, where x and y are vectors of length n.

The properties of inner product that you need to know are:

1. Commutativity: <x,y> = <y,x>
This means that the order in which the vectors are multiplied does not affect the result of the inner product.

2. Linearity: <ax + by, z> = a<x,z> + b<y,z>
This property states that the inner product is linear, meaning that it follows the rules of addition and multiplication.

3. Positive definiteness: <x,x> ≥ 0
This property ensures that the inner product is always positive or zero, with the exception of the zero vector.

4. Orthogonality: <x,y> = 0 if x and y are orthogonal
If two vectors are orthogonal, their inner product will be zero. This property is useful in determining whether two vectors are perpendicular to each other.

5. Non-degeneracy: <x,y> = 0 only if x = 0 or y = 0
This property states that the inner product is only zero if one of the vectors is the zero vector. Otherwise, it will always produce a non-zero value.

There are other properties of inner product, such as conjugate symmetry and antilinearity, but these are the most commonly used ones.

I hope this helps in understanding the properties of inner product. If you have any further questions, please feel free to ask. Good luck with your studies!