- #1
Lindsayyyy
- 219
- 0
Hi everyone
I have a quantum state
[tex] \mid \Psi \rangle= a_1 \mid \Psi_1 \rangle + a_2 \mid \Psi_2 \rangle[/tex]
wheres as psi1 and psi are normalized orthognal states.
Not I want to express the psi with the following two states
[tex] \mid \Psi_3 \rangle = \frac {1}{\sqrt{2}} ( \mid \Psi_1 \rangle +\mid \Psi_2 \rangle)[/tex]
and
[tex] \mid \Psi_3 \rangle = \frac {1}{\sqrt{2}} ( \mid \Psi_1 \rangle -\mid \Psi_2 \rangle)[/tex]
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Well, I don't have much of an idea actually. I know how to calculate coefficients if I have different basis vectors, but that doesn't seem to help here. Can anyone give me a little hint on how to approach this?
Thanks for your help
Homework Statement
I have a quantum state
[tex] \mid \Psi \rangle= a_1 \mid \Psi_1 \rangle + a_2 \mid \Psi_2 \rangle[/tex]
wheres as psi1 and psi are normalized orthognal states.
Not I want to express the psi with the following two states
[tex] \mid \Psi_3 \rangle = \frac {1}{\sqrt{2}} ( \mid \Psi_1 \rangle +\mid \Psi_2 \rangle)[/tex]
and
[tex] \mid \Psi_3 \rangle = \frac {1}{\sqrt{2}} ( \mid \Psi_1 \rangle -\mid \Psi_2 \rangle)[/tex]
Homework Equations
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The Attempt at a Solution
Well, I don't have much of an idea actually. I know how to calculate coefficients if I have different basis vectors, but that doesn't seem to help here. Can anyone give me a little hint on how to approach this?
Thanks for your help