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## Main Question or Discussion Point

what is the physical significance of othogonality condition? or what is meant when we say that two eigen states are orthogonal?

- Thread starter sruthisupriya
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what is the physical significance of othogonality condition? or what is meant when we say that two eigen states are orthogonal?

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George Jones

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Here's one thing. Suppose that two orthogonal eigstates of the observable A correspond to distinct eigenvalues a1 and a2. Perform a meausurement of A and assume that the result is a1. Perform a second measurement of A immediately after the first measurement. The probabilty that the result is a2 is zero.what is the physical significance of othogonality condition? or what is meant when we say that two eigen states are orthogonal?

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If I can measure certain eigenstates, the probability of measuring a particle in the state [tex]|\Psi\rangle[/tex] and obtaining it being in the state [tex]|\phi\rangle[/tex] after measurement is

[tex] P(\phi) = |\langle \phi | \Psi \rangle|^2 [/tex]

So what if these two states are orthogonal to each other?

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reilly

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Regards,

Reilly Atkinson

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In the case of degeneracy, such as with unpaired electron spin not in a magnetic field, the situation is a little more complicated, because the degenerate orthogonal solutions can mix.

-Jim

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