# De Broglie relations for particle under potential

The de Broglie relations connecting the wave-particle dual nature as generalised from photons to all matter particles are given by $$E=\hbar\omega$$ and $$p=\hbar k$$ (Characterizing a single plane wave with wave parameters $$\omega$$ and $$k$$ .)

Are these relations true for a time dependent potential $$V(x,t)$$ And if yes then is there any proof, if not then can we say that de Broglie's relations are hypotheses?

• Suppose $V(x)$ is such that its maximum value is less than energy eigenvalue $E$. Then what happens to the de Broglie relations? Nov 23, 2020 at 8:54
• But we can still have plane waves when we have constant potential $V_0$ Nov 25, 2020 at 20:56