Solution
= Solution
For a plane wave $\phi=e^{i(kx-\omega t)}$, the <Klein-Gordon equation> gives
$$
-\omega^2+c^2k^2+A^2c^2=0.
$$
Thus the positive-frequency dispersion relation is
$$
\boxed{\omega(k)=c\sqrt{k^2+A^2}}.
$$
= Solution
For a plane wave $\phi=e^{i(kx-\omega t)}$, the <Klein-Gordon equation> gives
$$
-\omega^2+c^2k^2+A^2c^2=0.
$$
Thus the positive-frequency dispersion relation is
$$
\boxed{\omega(k)=c\sqrt{k^2+A^2}}.
$$