Quantum evolution near unstable equilibrium point: an algebraic approach
Zai-Qiao Bai, Wei‐Mou Zheng · Journal of Physics A Mathematical and General · 2003
We study the quantum evolution of an unstable system in su(1, 1) algebra: The evolution of any initial state \k, v> is recursively obtained. When t --> infinity, \\(2) decays as e(-4vt) or t(-4v) in the hyperbolic (H = 2K(1)) or parabolic (H = 2K(1) + 2K(3)) unstable cases, respectively. The quantum-classic correspondence independent of the Bargmann index v is established based on the long-time and large-scale behaviour of wavefunctions.