So what exactly is a complex number?

[Francesco Guerrieri]

On 9/3/07, Wildemar Wildenburger <lasses_weil at klapptsowieso.net> wrote:
>
> Grzegorz Słodkowicz wrote:
> > In fact, a proper vector in physics has 4 features: point of
> > application, magnitude, direction and sense.
> >
> OK, help me out here: What 'direction' does |Ψ> (a state-vector in
> quantum mechanics) have? Also, doesn't sense directly follow from the
> point of application.


For instance, you can apply a force to a point and it can be "outward" or
"inward".

The direction of a state vector is completely specified by its decomposition
(given finite norm and completeness of the basis), just like ordinary
vectors.
But since actually in quantum mechanics you are dealing with unit rays and
everything is defined up to a phase (which could be relevant given the topic
of this thread!)... I'd say that kets are not the most recommendable way to
introduce the concept of vector, or of complex variables :-)

francesco
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