# Physical significance of othogonality condition?

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

George Jones
Staff Emeritus
Gold Member
what is the physical significance of othogonality condition? or what is meant when we say that two eigen states are orthogonal?

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.

Think about the postulates of quantum mechanics:

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

$$P(\phi) = |\langle \phi | \Psi \rangle|^2$$

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

reilly