Expand ψ(o) in terms of eignestates

[M. next]

if ψ(o)=(1 0)^{T} at time t=0.

According to some Hamiltonian, it was found that the corresponding eigenstates are |ø_{1}> = 1/√2(1 i)^{T} and |ø_{2}> = 1/√2(1 -i)^{T}<br /> <br /> so then we wanted to expand ψ(0) in terms of |ø_{1}&gt; and |ø_{2}&gt;:<br /> <br /> the author got: 1/√2|ø_{1}&gt; + 1/√2 |ø_{2}&gt;<br /> <br /> My question is that where did he get the coefficients of |ø_{1}&gt; and |ø_{2}&gt;?? Is there a certain rule to this?<br /> <br /> Note: this is an easy example, I can give a more detailed one if needed.

 

[ChrisVer]

Just solved this:
\psi(0)= a |1&gt; + b |2&gt;
for a,b