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受线性阻尼和含时外力作用粒子的量子行为
Quantum behaviors of the particles affected by the linear-damping and time-dependent external force
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摘要: 运用广义线性量子变换理论求解了采用两种不同正则化变换给出的受线性阻尼和含时外力作用粒子的哈密顿量;给出了演化算符的严格解,以及粒子坐标和动量的期望值、量子涨落.结果表明：1）两种正则化变换是等价的;2）线性阻尼对粒子的动量存在压缩效应,动量的偏差随时间t按负指数规律衰减,阻尼系数越大,衰减越快;3）粒子坐标和动量的期望值与经典值相同.Abstract: In this paper,we handle the Hamiltonian of the particles that are affected by the linear-damping and time-dependent external force given by two different canonical transformations by using the theory of generalized quantum linear transformation.We give the rigorous solution of evolution operator,and the expectation values of coordinate and momentum of the particles quantum fluctuations.Results show that 1） the two regular translations are equivalent;2） linear damping has a squeezing effect on the momentum of particle,and the deviation of the momentum attenuates with time t according to the rule of negative exponent,and the bigger the damping coefficient, the faster the attenuation is;3） the expectation values of coordinate and momentum of the particle are equal to their classical values correspondingly.
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