... e(ˆA+ˆB)s+12[ˆA,ˆB]s2Setting s = 0, we obtainˆF (0) =ˆI. Finally substitutingˆF (0) and s = 1, we obtain therequired result.• (d) Prove the following identity for any two operatorsˆA ... useful propertiesδ(x) = δ(−x)Preface In this course, we cover the necessary mathematical tools that underpin modern theoretical physics. We examine topics in quantum mechanics (with which you have ... self-adjoint• Find an expression forˆH2 in terms ofˆHAnswer: Use the anti-commutator property ofˆQ to getˆH2= αˆH.• Deduce the eigenvalues ofˆH using the results obtained above.Answer:The...