jamie.j1989
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Hi, I'm doing a project on graphene and don't really understand why we use the Dirac equation instead of the Schrödinger equation. The fermi velocity of electrons in graphene is not relativistic, I know the particles are considered as quasiparticles but don't see how this changes things. My only reasoning is that the effective mass is zero and the 1/m dependence in the Schrödinger equation is incompatible with this? Thanks.
Scrodinger equation
$$i\hbar\frac{\partial}{\partial{t}}\psi({\textbf{r},t})=\left[-\frac{\hbar^2}{2m}\nabla^2V(\textbf{r})+E\right]\psi({\textbf{r},t})$$
Dirac equation
$$\left[\gamma^{\mu}\partial_{\mu}+\frac{c}{\hbar}m\right]\psi(\textbf{r},t)=0$$
Scrodinger equation
$$i\hbar\frac{\partial}{\partial{t}}\psi({\textbf{r},t})=\left[-\frac{\hbar^2}{2m}\nabla^2V(\textbf{r})+E\right]\psi({\textbf{r},t})$$
Dirac equation
$$\left[\gamma^{\mu}\partial_{\mu}+\frac{c}{\hbar}m\right]\psi(\textbf{r},t)=0$$