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.