Re: [Phys-l] unit vector notation

[John Denker <jsd@av8n.com>]

On 08/17/2007 03:37 PM, Rauber, Joel wrote:
> Opinions and discourse wanted on unit vector notation for the 
> introductory course.
>
> Common variants:
>
> i_hat, j_hat, k_hat
>
> x_hat, y_hat, z_hat
>
> e_x, e_y, e_z
>
> e_1, e_2, e_3

> others?

Other common variants include:

 -- You can use i,j,k without hats.  
  (Some people wear silly hats at parties.  
  I don't think vectors should wear silly hats.)

 -- The Clifford algebra literature likes to use gamma_1, gamma_2, gamma_3.

I rewrote this section
  http://www.av8n.com/physics/intro-vector.htm#sec-basis-names
to discuss this issue ... including comments on why the subscripted
names are preferred, especially in non-introductory courses:

] The practice of using subscripts to denote /which/ basis vector is
] established in the math and physics community and is unlikely to
] change anytime soon The obvious disadvantage is that is a
] never-ending source of confusion for students. The practice does
] however have some significant advantages, such as allowing
] expressions such as equation 5 to be written more compactly....

=======================================

> In introductory physics I certainly don't want to use
>  
> <e_x|v>  the inner product, in lieu of v_x
>  
> or  |e_x><e_x|v>  in lieu of v_x with an arrow over it.  Or similar such
> notations.


Point taken.  I rewrote this section:
  http://www.av8n.com/physics/intro-vector.htm#sec-projections-elements
to use plain old dot products rather than bra-ket notation.


  (I want to discuss the issue of row vectors versus column
  vectors, but it shouldn't be conflated with the discussion
  of projection operators.)