# Green's function for the wave function

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## Main Question or Discussion Point

We want to solve the equation.
$$H\Psi = i\hbar\frac{\partial \Psi}{\partial t}$$ (1)

If we solve the following equation for G

$$(H-i\hbar\frac{\partial }{\partial t})G(t,t_{0}) \Psi(t_{0}) = -i\hbar\delta(t-t_{0})$$ (2)

The final solution for our wave function is,

$$\Psi(t) = G(t,t_{0})\Psi(t_{0})$$ (3)

I don't understand the steps. How do we get from (2) to (3) ?

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Orodruin
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