What is the physical significance of having +/- a constant multiplying

[Whistlekins]

After normalising a wave equation, let's say psi = A*e^(-r/a), and finding that A = +/- sqrt(2/a), what does this mean in terms of the physical significance of the wave?

Would the wave just be a superposition of two waves with the two different A values?

 

[jtbell]

You can multiply any wave function by a constant factor of the form $e^{i\theta}$ without any physical effect. For example, the probability density gets multiplied by $e^{i\theta}e^{-i\theta} = 1$ which of course has no effect.

As a special case of the above, if you let $\theta = \pi$, the constant factor becomes $e^{-i\pi} = -1$.