A Spherical Tensor Problem

Since last I wrote about it, my continued sojourn through Sakurai has brought me back to spherical tensors, a topic I didn’t well understand when last I saw it. The problem in question is Sakurai 3.21. We will get to this problem shortly… I’ve been thinking about how best to include math on this blog. […]

Schwinging the Pendulum

Masses on springs get a lot of use in physics; you see them early in that first year of introductory classical mechanics with Hooke’s law and they come back over and over again after that. Physicists are fond of saying that basically everything in reality reduces to a mass on a spring if you squint […]

Angular momentum by harmonic oscillator

I’ve been thinking about Sakurai problem 3.19 for the past few days. The problem reads: 19.) What is the physical significance of the operators K+ ≡ a+†a-†        and       K- ≡ a+a- in Schwinger’s Scheme for angular momentum? Give nonvanishing matrix elements of K± I’m not sure I completely understand this problem yet. The ‘a’ operators […]

Spherical Harmonics and State Rotation

Working my way through Sakurai problem 3.18. I spent quite a bit of time thinking about how exactly to interpret the math that underlies this problem. Here’s the problem as written in my notebook: “18.) Consider an orbital angular momentum eigenstate |l=2, m=0>. Suppose this state is rotated by an angle beta about the y-axis. […]