What Does A Represent in the Quantum Mechanical Wave Equation Ae^{i(kx-wt)}?

[velo city]

What is the "A" in the wave equation: $Ae^{i(kx-wt)}$? What does it mean in quantum mechanics? Is it just the amplitude?

 

[Matterwave]

In quantum mechanics, it would normally be a normalization constant. Except, if that wave equation were taken to be over all space, it is not normalizable.

So under some circumstances, you can think of it like an amplitude, for problems involving, e.g. scattering. But only ratios should ever be used if we are using plane wave approximations.

 

[bhobba]

What is the "A" in the wave equation: $Ae^{i(kx-wt)}$? What does it mean in quantum mechanics? Is it just the amplitude?

A is sometimes (but not always) set by where you got it from eg if you are considering a state of definite momentum that is modeled by Dirac Delta function it determines A in the position representation eg:
http://hitoshi.berkeley.edu/221a/delta.pdf

But sometimes that's not the case eg (see section 7.7 on the free particle):
http://www.colorado.edu/physics/TZD/PageProofs1/TAYL07-203-247.I.pdf

However by looking at the momentum representation of the solution that would naturally set the value of the constant via the Dirac Delta function.

It must always be remembered such states don't really exist, they are mathematical fictions introduced for convenience.

Thanks
Bill