Consider a two-dimensional Hilbert space. Operator A that acts on states in this Hilbert space has eigenvectors |a₁) and la2), with eigenvalues a₁ and a respectively, while operator B has eigenvectors b₁) and b₂) with eigenvalues b₁ and b₂, that are related to those of A as: |b₁)=√(2|a₁) +3|a2)) |b₂)=√(3|a₁) - 2|a2)) An experiment is done where first the operator A is measured, and let's say the outcome is a2. Immediately afterwards, operator B is measured. What is probability of finding the eigenvalue bi when B is measured?

Consider a two-dimensional Hilbert space. Operator A that acts on states in this Hilbert space has eigenvectors |a₁) and la2), with eigenvalues a₁ and a respectively, while operator B has eigenvectors b₁) and b₂) with eigenvalues b₁ and b₂, that are related to those of A as: |b₁)=√(2|a₁) +3|a2)) |b₂)=√(3|a₁) - 2|a2)) An experiment is done where first the operator A is measured, and let's say the outcome is a2. Immediately afterwards, operator B is measured. What is probability of finding the eigenvalue bi when B is measured?