1. The problem statement, all variables and given/known data Consider a particle with mass m oscillates in a simple harmonic potential with frequency ω. The position, x, and momentum operator, p, of the particle can be expressed in terms of the annihilation and creation operator (a and a† respectively): x = (ħ/2mω)^0.5 * (a† + a) p = i(ħmω/2)^0.5 * (a - a†) The annihilation and creation operators satisfy the following commutation relations: [a,a†] = 1 The eigenvalue equation of a is found as: a|α> = α|α> Where |α> is a coherent state a) Find the expectation value <a†> in coherent state |α> b) Find the expectation values of <aa>, <a†a>, and <a†a†> c) Calculate the uncertainty relation (<(x-<x>)2><(p-<p>)2>)0.5 2. Relevant equations Relevant equations given above 3. The attempt at a solution I've worked through most of the problem and only noticed that I may have done something wrong when I got to part c, where the expression that I get for <x> causes the expectation value <(x-<x>)2> to be equal to 0, which also means the uncertainty relation is equal to 0. I think the error may be when I wrote the eigenvalue equation for a in bra notation like this: <α|a† = <α|α* Is this the correct way of expressing the eigenvalue equation given in the question in bra notation?