It was my son's fault. He has been working on a project where the Wigner function is routinely invoked. He and now I am trying to understand its meaning. It was with some excitement that I located a thirty-year-old paper on the physical interpretation of the Wigner function. The combination of eating chocolates and having wine with dinner in the midst of my restricted carbohydrate diet reved up my metabolism. The paper, on the other hand, reved up my already racing mind. I was kept wide awake for most of the night in a frenzied state even after taking a dose of zolpidem and lorazepam tartrate.
Dirac notation is one of the most beautiful ways to formulate quantum mechanics because of its generality. A wavefunction, for example, represents all that we can know know about a system in terms of coordinates, such as the position or momentum. A state vector, on the other hand, is a general quantity whose projection onto the position axis gives the wavefunction as a function of position or a projection along the momentum axis gives a function of momentum. Since the Wigner function depends on momentum and position, I played mathematical tricks in my mind to represent it in the more general operator form.
One thing let to another, and I was trying to find ways to make transformations into a variety of forms that would give me insights. I played tricks by inserting closure, or used the inverse process of turning a variable into an operator so that I could collapse a sum with closure. I could not stop myself from making sense of the equations that tumbled around in my head. Eventually, sleep took its hold, but its grasp week. I woke tired, but looking forward to transcribing my ideas onto paper.
We are now packing and getting ready to fly back to Pullman. Though I am weary, an air of optimism fills my spirit that perhaps I will understand something new today. For now, my worries are tucked away in a hidden place.