科研之友
微信
新浪微博
Facebook
分享链接
摘要
In its geometric form, the Maupertuis Principle states that the movement of a classical particle in an external potential V(x) can be understood as a free movement in a curved space with the metric g(mu nu)(x) = 2M[V(x) - E]delta(mu nu). We extend this principle to the quantum regime by showing that the wavefunction of the particle is governed by a Schrodinger equation of a free particle moving through curved space. The kinetic operator is the Weyl-invariant Laplace-Beltrami operator. On the basis of this observation, we calculate the semiclassical expansion of the particle density.
- 出版日期2014-9
