the free particle Schrodinger equation describes a non istic matter wave without forces (no potential energy). Remember, when we considered plane wave solutions, the Schrodinger equation was consistent with the non-relativistic energy of a free particle: E = p2/2m. Now let's try finding a relativistic wave equation! To do this, start with a plane wave with the form = ei(kx-wt) where k = p/ħ and w = E/ħ and try to find a differential equation that yields the correct relativistic energy expression when applied to this plane wave. It will be useful to consider the relativistic energy squared: E² = p²c² + m²c². 4. We can always write the wavefunction as V = V₁ +iV2 where ₁ and ₂ are real functions. Using the one-dimensional free particle Schrodinger equation, what equations should ₁ and ₂ satisfy?

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