(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider the simplified wave function: [tex]\psi (x,t) = Ae^{i(\omega t - kx)}[/tex]

Assume that [tex]\omega[/tex] and [tex]\nu[/tex] are complex quantities and that k is real:

[tex]\omega = \alpha + i\beta[/tex]

[tex]\nu = u + i\omega[/tex]

Use the fact that [tex] k^2 = \frac{\omega^2}{\nu^2}[/tex] to obtain expressions for [tex]\alpha[/tex] and [tex]\beta[/tex] in terms of [tex]u[/tex] and [tex]\omega[/tex].

2. Relevant equations

i[tex]\psi (x,t) = Ae^{i(\omega t - kx)}[/tex]

ii[tex]\omega = \alpha + i\beta[/tex]

iii[tex]\nu = u + i\omega[/tex]

iv[tex] k^2 = \frac{\omega^2}{\nu^2}[/tex]

3. The attempt at a solution

I cannot seem to find expressions for [tex]\alpha[/tex] and [tex]\beta[/tex] in terms of [tex]u[/tex] and [tex]\omega[/tex]. I have tried rearranging the given equations in many such ways, but have not come up with any conclusive result.

Any suggestions are greatly appreciated. Thank you.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Solving Wave Equation / Imaginary Numbers

**Physics Forums | Science Articles, Homework Help, Discussion**