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首页> 外文期刊>Nuclear physics, B >Exact semiclassical evolutions in relativistic and non-relativistic scalar quantum mechanics and quantum cosmology
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Exact semiclassical evolutions in relativistic and non-relativistic scalar quantum mechanics and quantum cosmology

机译：相对论和非相对论标量量子力学和量子宇宙学中的精确半经典演化

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The necessary and sufficient conditions for the exactness of the semiclassical approximation for the solution of the Schrodinger and Klein-Gordon equations are obtained, It is shown that the existence of an exact semiclassical solution of the Schrodinger equation determines both the semiclassical wave function and the interaction potential uniquely up to the choice of the boundary conditions. This result also holds for the Klein-Gordon equation. Its implications for the solution of the Wheeler-DeWitt equation for the FRW scalar field minisuperspace models are discussed. In particular, exact semiclassical solutions of the Wheeler-DeWitt equation for the case of massless scalar field and exponential matter potentials are constructed, The existence of exact semiclassical solutions for polynomial matter potentials of the form lambda phi(2p) is also analyzed. It is shown that for p = 1, 2 and 3, right-going semiclassical solutions do not exist, A generalized semiclassical perturbation expansion is also developed which is quite different from the traditional (h) over bar and M-p(-1) expansions. (C) 1998 Published by Elsevier Science B.V. [References: 50]
机译：得到了Schrodinger和Klein-Gordon方程解的半经典近似精确性的充要条件，证明了Schrodinger方程的精确半经典解的存在决定了半经典波动函数和相互作用。势唯一取决于边界条件的选择。该结果也适用于Klein-Gordon方程。讨论了其对FRW标量场微型超空间模型的Wheeler-DeWitt方程解的含义。特别是构造了无质量标量场和指数势的情况下Wheeler-DeWitt方程的精确半经典解，并且分析了λphi（2p）形式的多项式势的精确半经典解的存在。结果表明，对于p = 1、2和3，不存在向右的半经典解，还开发了广义的半经典扰动展开，它与传统的（h）bar和M-p（-1）展开完全不同。 （C）1998由Elsevier Science B.V.出版[参考：50]

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