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- Homework Statement
- I want to show that the inner product between the plane wave solution and its conjugate is zero.

- Relevant Equations
- The inner product is defined as ##(u_{\vec{k}},u_{\vec{k}'})=-i\int u_{\vec{k}}\partial_{t}u^{*}_{\vec{k}'}-u^{*}_{\vec{k}'}\partial_{t} u_{\vec{k}}\,\mathrm{d}^3 x##

The unormalised plane wave solution is given as ##u_{\vec{k}}=e^{i\vec{k}\cdot\vec{x}-i\omega t}##. I want to show that ##(u_{\vec{k}},u^{*}_{\vec{k}'})=0##. However, I don't seem to be able to get the answer through direct calculation. Any hints on how to obtain the answer?