(C) (H You learn about ladder operators in the context of the quantum harmonic oscillator in Peter's half of the course. A fellow student pitches a clever idea, which is a hypothetical pair of ladder operators 6+ and q for quantum spin, that looks something like: '9': = a} i {cry Obtain the corresponding matrices for the two ladder operators {3+ and o. and show using four examples that they work on the states In) and Id) as intended. If you need to add any numerical prefaetors or other 'correetions' to the hypothetical 5+ and o' to get things to work properly, e.g., have unitarity or conserve normalisation, please do so. [4 marks] The ladder operators 5+ and {I that you get in (e) are obviously not Hermitian. Is this a problem? Briey explain why or why not. [1 mark]