Suppose the system is initially in state $|a$: at $t=0.$ Now we want to express the quantum state at a time $t>0$

in the basis of $\{|a$:$),|b$:$.$ That is$,$

$|r(t)$: where $k$ and $l$ are complex numbers.

And at $t=0,k=1$ and $l=0.$

Write down the expression for $k$ in terms of $a,b,$ sigma, imaginary unit $i,$ reduced Planck's constant, $\frac{h}{b}ar,$ and

time $t.$ Note that your answer does not have to include all of these variables.

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