- #1
forhad_jnu
- 2
- 0
I need to elaborate the equation ,and need to know what is the physical significance and how matrices will manipulate in the equation $$
\hat{H} = (\hat{\tau_3}+i\hat{\tau_2})\frac{\hat{p}^2}{2m_0}+ \hat{\tau_3}m_0 c^2 = \frac{\hat{p}^2}{2m_0}
\left| \begin{array}{ccc}
1 & 1 \\
-1 & -1 \\
\end{array}\right| \frac{\hat{p}^2}{2m_0} + \left| \begin{array}{ccc}
1 & 0 \\
0 & -1 \\
\end{array}\right| m_0 c^2
$$
Where $$\tau_1 , \tau_2,\tau_3
$$ are Pauli matrices and Hamiltonian comes from "Schrodinger form of the free Klein_Gordon equation
And also why did we added Pauli matrices in the free Hamiltonian ?
\hat{H} = (\hat{\tau_3}+i\hat{\tau_2})\frac{\hat{p}^2}{2m_0}+ \hat{\tau_3}m_0 c^2 = \frac{\hat{p}^2}{2m_0}
\left| \begin{array}{ccc}
1 & 1 \\
-1 & -1 \\
\end{array}\right| \frac{\hat{p}^2}{2m_0} + \left| \begin{array}{ccc}
1 & 0 \\
0 & -1 \\
\end{array}\right| m_0 c^2
$$
Where $$\tau_1 , \tau_2,\tau_3
$$ are Pauli matrices and Hamiltonian comes from "Schrodinger form of the free Klein_Gordon equation
And also why did we added Pauli matrices in the free Hamiltonian ?