Question

Solutions to schrodinger equation are labelled with

Answer 1

Answer:

I am confused by the comments. Perhaps I am missing something.

For any linear differential equation with a given solution, a constant times that solution is also a valid solution.

The Schroedinger equation is a linear differential equation for the wavefunction Ψ. This means that if Ψ is a solution then so is AΨ where A is a complex constant. You can fix this constant by further requirements like the normalization condition ∫ddx|Ψ|2=1. Of course as Peter Morgan said, the phase of A remains undetermined by the normalization condition.

I think this is also what Griffiths means. I quote him after he says that the wavefunction should be normalized since the particle has to be somewhere.

Well, a glance at Equation 1.1 [the Schroedinger equation] reveals that if Ψ(x,t) is a solution, so too is AΨ(x,t), where A is any (complex) constant.

and then he goes on to say that we must pick A such that the wavefunction is normalized.