Approximate formulas for expectation values using coherent states

作者：Foggiatto A L; Angelo R M; Ribeiro A D^*

来源：Progress of Theoretical and Experimental Physics, 2017, 2017(10): 103A01.

DOI：10.1093/ptep/ptx129

• A02
• A60

For time-independent Hamiltonians, the dynamics of quantum expectation values of observables in coherent states (A) over barT can be easily represented as an integral formula involving forward and backward propagators K-+/-. In the semiclassical regime, an approximate formula (A) over bar (sc)(T) can be constructed via the replacement of K-+/- by their semiclassical versions, followed by a consistent integration procedure. Alternatively, one can keep the original propagators and rewrite the integral formula for (A) over barT as a truncated series expansion, thus introducing a new approximate formula (A) over bar (se)(T). Yet a third approximation (A) over bar (cl)(T) can be derived by use of a classical statistical approach based on the Liouville equation and Gaussian probability distributions. In the present paper, we develop these three approximate formulas for expectation values, apply them to simple systems, and evaluate their accuracy.

• 出版日期2017-10