Quantum Hamiltonian for the Rigid Rotator

J. Denmead Smith

K. N. Srinivasa Rao, D. Saroja

Makito Oi

Nuclear rotation is revisited to seek for a new perspective.Review is made first for the basic concept of the nuclear rotation.Then, the quantization procedure of the rigid-body Hamiltonian is reviewed for a quantum mechanical understanding of the dynamics of rigid-body rotations.A linear rigid body is then investigated and its motion is studied from classical and quantum viewpoints.Finally, an application of the linear rigid-body rotation is attempted for a description of elongated nuclear systems, such as Beryllium 8, a two-alpha-cluster system.

Harish Parthasarathy

Express the velocity of each point of a rigid body in terms of the time derivative of the rotation matrix applied to the initial position of the point and hence integrate its norm square over the entire rigid body to obtain the kinetic energy of the rigid body as a quadratic function of the time derivative of the rotation matrix with the quadratic function being determined in terms of the moment of inertia matrix of the body. Express the gravitational potential of the rigid body as a linear function of the rotation matrix and hence determine the total Lagrangian of the body in terms of the instantaneous rotation matrix and its time derivative. Perform the Legendre transformation on this Lagrangian to obtain the Hamiltonian of the rigid body in terms of the Lie algebra coordinates and their corresponding canonical momenta.

Tsunehiro Kobayashi, Takashi Suzuki

P. Gulshani, DAVID J. ROWE

The Hamiltonian describing a system of particles in a rotating coordinate system is derived and it is shown that the simple classical solution of rigid flow is forbidden in quantum mechanics, even at very low angular velocities. This effect is closely parallel to the Aharonov–Bohm effect, which likewise has its origin in the single-valuedness requirement of the wave function. An analytical approach to perturbation theory is used to include the effects of the Coriolis and centrifugal forces and to derive the current flows for some independent-particle systems, that is, for the Inglis cranking model. It is shown, by explicit construction, that the currents are not rigid even when the moment of inertia assumes the rigid-flow value, as it does for the harmonic oscillator single-particle potential under conditions of self-consistency. Furthermore, it is shown that, for a more general potential, even the moment of inertia is not rigid.