What does H12*C2 mean in Feynman's equation 8.43?

[mkbh_10]

In the volume III of R Feynman series which is on Quantum Mechanics , please explain to me the eq.8.43 given on page 1529, i know how we got the equation but the 2nd part of 1st equation (H12)C2, what does it mean ?

 

[Gokul43201]

This equation is simply an application of eq. 8.39 to a 2-state system. C1 and C2 are the components of the wave function along each of the 2 basis states. H12 and H21 are the off-diagonal terms in the Hamiltonian. $$<br /> \mathcal{H} \equiv \left(<br /> \begin{array}{cc}<br /> H_{11} & H_{12}\\<br /> H_{21} & H_{22}<br /> \end{array}<br /> \right)<br />$$