The Quantum Mechanics of Many-Body Systems: Second Edition (Dover Books on Physics) by Thouless D.J

Author:Thouless, D.J. [Thouless, D.J.]
Language: eng
Format: epub
Publisher: Dover Publications
Published: 2013-12-03T00:00:00+00:00

where ω is the angular velocity of rotation and L is the angular momentum operator. To find steadily rotating solutions of the equations one can look for solutions of Eq. (5.78) that are stationary in the rotating coordinate system. A stationary solution of Eq. (5.72) is obtained by finding the determinant which minimizes the expectation value of the Hamiltonian H, and so a stationary solution of Eq. (5.78) can be found by minimizing the expectation value of H – ω · L. In general, this solution will not be symmetrical about the axis of rotation, so it must represent a steadily rotating system.

If the angular velocity ω is small, the departure of ρ (measured in the rotating system) from its equilibrium value in the stationary system can be obtained as a power series in ω. It must have the form given by Eq. (5.74), to lowest order in ω, and substitution of this in Eq. (5.78) gives

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