Final answer:
When you are given a linear combination of psi, you can determine the probabilities associated with each eigenvalue using the Born rule.
Step-by-step explanation:
According to the Born rule, the probability of measuring an eigenvalue is equal to the square of the absolute value of the coefficient of that eigenvalue in the linear combination.
For example, suppose you have a linear combination of wavefunctions psi = c1 * psi1 + c2 * psi2, where c1 and c2 are complex numbers and psi1 and psi2 are eigenvectors with eigenvalues λ1 and λ2, respectively.
The Born rule states that the probability of measuring eigenvalue λ1 is |c1|^2 and the probability of measuring eigenvalue λ2 is |c2|^2.
For a more general case with multiple eigenvalues and their associated probabilities, you would apply the Born rule to each eigenvalue to calculate the corresponding probabilities.