I am self studying the Book- Introduction to Quantum Mechanics , 2e. Griffith. Page 47. While the book has given a proof for eq. 2.64 but its not very ellaborate Integral(infinity,-infinity) [f*(a±g(x)).dx] = Integral(infinity,-infinity) [(a±f)* g(x).dx] . It would be great help if somebody could provide me a more step by step proof of the same. Where a+ and a- are roots of Hamiltonian of harmonic oscillator problem.