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Expand ψ(o) in terms of eignestates

  1. Mar 2, 2014 #1
    if ψ(o)=(1 0)[itex]^{T}[/itex] at time t=0.

    According to some Hamiltonian, it was found that the corresponding eigenstates are |ø[itex]_{1}[/itex]> = 1/√2(1 i)[itex]^{T}[/itex] and |ø[itex]_{2}[/itex]> = 1/√2(1 -i)[itex]^{T}

    so then we wanted to expand ψ(0) in terms of |ø[itex]_{1}[/itex]> and |ø[itex]_{2}[/itex]>:

    the author got: 1/√2|ø[itex]_{1}[/itex]> + 1/√2 |ø[itex]_{2}[/itex]>

    My question is that where did he get the coefficients of |ø[itex]_{1}[/itex]> and |ø[itex]_{2}[/itex]>?? Is there a certain rule to this?

    Note: this is an easy example, I can give a more detailed one if needed.
     
  2. jcsd
  3. Mar 2, 2014 #2

    ChrisVer

    User Avatar
    Gold Member

    Just solved this:
    [itex] \psi(0)= a |1> + b |2> [/itex]
    for [itex]a,b[/itex]
     
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