Geometrization of the Schrödinger equation
| Autor: | Hagen Kleinert, Antonia Karamatskou |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
Physics
curved space quantum mechanics Free particle Quantum field theory in curved spacetime Physics and Astronomy (miscellaneous) geometric physics Operator (physics) Schrödinger equation in curved space Semiclassical physics quantum particle motion in curved space exact solutions Schrödinger equation symbols.namesake Classical mechanics Maupertuis' principle symbols Hamilton–Jacobi–Einstein equation Curved space |
| Popis: | 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 gμν(x) = 2M[V(x) - E]δμν. We extend this principle to the quantum regime by showing that the wavefunction of the particle is governed by a Schrödinger 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. |
| Databáze: | OpenAIRE |
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