Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Gold Member

    Just solved this:
    [itex] \psi(0)= a |1> + b |2> [/itex]
    for [itex]a,b[/itex]
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook