1. The problem statement, all variables and given/known data Using Dirac Notation prove for the Hermitian operator B acting on a state vector |ψ>, which represents a bound particle in a 1-d potential well - that the expectation value is <C^2> = <Cψ|Cψ>. Include each step in your reasoning. Finally use the result to show the expectation value of the kinetic energy of the particle in the state |ψ> is <Ekin> = (1/2m)<Pψ|Pψ> ???? Can someone enlighten my thought via a diagram exactly what I am looking at pls 2. Relevant equations I have to find the right eqns, which I guess are the Hermitian related eqns: stating what is Hermitian <a|Cb> = <Ca|b> , where C is operator, a and b are normalisable functions. <a|λCb> = λ<a|Cb> , where λ is a real constant. any power of C is Hermitian 3. The attempt at a solution My attempt has been quite measely as I cannot get any visual sense of it. (ideas???) So> To prove the <C^2> = <Cψ|Cψ>, all I can think to say is... The RHS with C being Hermitian. <Cψ|Cψ> = <ψ|CCψ> = <ψ|C^2ψ> As we are dealing with the same operator there is no difference if the order in which they so therefore obeys the requirement for a product to commute CC - CC = 0. therfore that will give the expectation value of <C^2> = <Cψ|Cψ>. Is that it or is there more reasoning? Turning to <Ekin> I have no idea what to do because it seems like the (1/2m) is just stuck in there because it previously known. Is there another reasoning?