# Does this equality have a name?

1. Feb 24, 2014

### M. next

Hey there,

I was wondering if this equality in QM has a name or not.

It goes as follows:

llψ+øll^2 + llψ-øll^2 = 2llψll^2 + 2lløll^2

where: ψ and ø are wave functions in Hilbert's space.

If it doesn't specifically have a name, what is its significance in QM?

Thankis

2. Feb 24, 2014

### WannabeNewton

It's just the parallelogram law. It has the usual geometric meaning and moreover if a norm satisfies it then the polarization identity can be used to define an inner product using the norm. The converse of course is trivial. This has nothing to do with QM it's just basic linear algebra.

3. Feb 24, 2014

### M. next

Oh, okay. I see! The reason, I said QM, is because I saw it in QM notebook. Thanks!