[mnq]

A particle is in a QM state ψ that is not an eigenfunction of the Energy operator H but is a superposition of eigenfunctions of the Energy operator ψ₁ and ψ₂ that have eigenvalues E₁ and E₂ so that ψ can be written as ψ = c₁ψ ₁ + c₂ψ ₂ where ψ ₁  and ψ ₂ are orthonormal, and c₁ and c₂ are expansion coefficients. What is the probability of getting E₁ as athe energy value for this QM state?

any help would be appreciated

[Juan R.]

A particle is in a QM state ψ that is not an eigenfunction of the Energy operator H but is a superposition of eigenfunctions of the Energy operator ψ₁ and ψ₂ that have eigenvalues E₁ and E₂ so that ψ can be written as ψ = c₁ψ ₁ + c₂ψ ₂ where ψ ₁  and ψ ₂ are orthonormal, and c₁ and c₂ are expansion coefficients. What is the probability of getting E₁ as athe energy value for this QM state?

any help would be appreciated

Start computing the energy of the system using the postulates of QM. Write down the expression and look for c₁ and c₂ therein.