1. The problem statement, all variables and given/known data We know: In a measurement of quantum mechanics (basic) the average value is the cosine of the angle between the orthonormal basis of the measurement apparatus and the qubit (vector) entering it. Question: How do we prove this? 2. Relevant equations 3. The attempt at a solution Can there be a mathematical proof to this? Or is this done by painstaking experiments in a laboratory? If you can answer this question, then I will know how to proceed. Thank you.