Rotating highly mixed Gaussian packets with minimal energy

We study two-dimensional quantum mixed Gaussian packets with a fixed value of mean angular momentum. Highly mixed packets, minimizing the mean energy of an isotropic oscillator with fixed mean angular momentum $\mathcal{L}$, are found under the condition that the inverse purity ${\mathcal{P}}^{-1}$ exceeds the sum $1+2\mathcal{L}$. These states can be considered rotating thermal states. Their statistical properties (such as variances of angular momentum and energy) are studied. The case of a charged particle in a homogeneous magnetic field is considered as well.