Can I assume this is a travelling wave?

[merry]

Hello,

I was solving the time dependent Schrödinger equation in a time-independent potential such that E<V and I got the following solution:

ψ = exp(-\sqrt{k}x - (iE/\bar{h})t)

where k > 0 and k = (2m/\bar{h}^{2})(V-E)

I was wondering if this was a left traveling wave i.e. whether I could write it as:
ψ = exp(-i (\sqrt{-k}x + (E/\bar{h})t) )

Would this be correct?

 

[zhermes]

No. Because you know that k is positive (and real), thus the simplest form is -\sqrt{k}, it means that as |x| increases, the wave-function is exponentially damped.