- #1
keen23
- 9
- 0
Hello!
once again I got trouble with Dirac-notation:
Given an non-orthonormal basis. Measurement via the projection operator should not give an definit answer, in which state the system was due to the overlap. Geometrical that's clear, but I'm unable to compute that... :(
I tried it for the following states:
[tex] |\psi_0\rangle=|0\rangle[/tex]
[tex]|\psi_1\rangle=\frac{1}{\sqrt{2}}(|0\rangle+|1\rangle)[/tex]
My projector looks the following way (I am not sure about the coefficients):
[tex]P=|0\rangle\langle0|+\frac{1}{2} (|0\rangle+|1\rangle)(\langle 0|+\langle 1|)[/tex]
And now I am confused. When I plug state psi1 on both sides I get a sum of several 0s and 1s I don't know how to interprete.
Any hints? Thank you!
once again I got trouble with Dirac-notation:
Homework Statement
Given an non-orthonormal basis. Measurement via the projection operator should not give an definit answer, in which state the system was due to the overlap. Geometrical that's clear, but I'm unable to compute that... :(
I tried it for the following states:
[tex] |\psi_0\rangle=|0\rangle[/tex]
[tex]|\psi_1\rangle=\frac{1}{\sqrt{2}}(|0\rangle+|1\rangle)[/tex]
Homework Equations
The Attempt at a Solution
My projector looks the following way (I am not sure about the coefficients):
[tex]P=|0\rangle\langle0|+\frac{1}{2} (|0\rangle+|1\rangle)(\langle 0|+\langle 1|)[/tex]
And now I am confused. When I plug state psi1 on both sides I get a sum of several 0s and 1s I don't know how to interprete.
Any hints? Thank you!