Question

answer part (b) please

The Dirac sandwich (220) is an expectation value 10.1 Imagine that you are writing a chapter for a textbook (as you have done many times before!). This time, you have to write a section showing how the 'Dirac sandwich,' which is of the form some state operator another state) is nothing but an expectation value. Your chapter should have the following sections. In all sections, make sure you give an example (or two!). (a) Explain what an eigenfunction expansion is. Make sure that along the way you explain the following ideas about vectors: • Basis vectors • Linear superposition • 'Spanning' a vector space In particular, make sure you make connections between the good old vectors are arrows with magnitude and direction model of vectors in 3D space and multi- dimensional vectors in a Hilbert space. (b) Define an expectation value in the context of games and winnings. Show how the idea carries over to the quantum world of n-channel Stern-Gerlach apparatuses. (c) Now, making use of all the definitions and ideas you have introduced in the previous two sections, complete the derivation and show how the Dirac sandwich is an expectation value. Calculate the expectation values of any of the spin-1/2 operators we have studied.