Matrix with fractions for indices?

[Shawnyboy]

Hi PF Peeps!

Something came up while I was studying for my QM1 class. Basically we want to represent operators as matrices and in one case the matrix element is defined by the formula :

$<m'|m> = \frac{h}{2\pi}\sqrt{\frac{15}{4} - m(m+1)} \delta_{m',m+1}$

But the thing is we know m takes on the fractional values -3/2, -1/2, 1/2, 3/2. So basically my question is simply put: can you have a matrix with fractions for indeces?

Thanks,
Shawn

 

[sk1105]

Yes you can. A matrix is essentially just a compact way of specifying what action to perform on each component of a vector to make another vector, and can contain whatever you want. Is there something you've seen or heard that made you think fractional indices weren't possible?

 

[jk22]

Maybe it is because your matrix represents a continuous operator hence having continuous indices ?

 

[theodoros.mihos]

I think your equation is not complete. If this is an eigenvalues equation then the diagonal matrix must have elements like:
$$ \sqrt{\frac{15}{4}-i(i+1)} $$where i the correspond to matrix column/row element by the same index on m values.
See also