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Particle’s wave function equation considered scalar potential and vector potential of Gravitational Field
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By the resolution of the geodesic line equation for external Gravitational Field, to get the gravitational field strength which contains scalar potential and vector potential as key parameters. Base on the field strength, Lagrangian L for the system of particle associate with the external Gravitational Field is constituted. Components which contribute to L are also discussed. Thus the Hamiltonian H is derived from L meanwhile the non-relativistic Hamiltonian of the system is concluded as well. Through the Hamiltonian H of system, Schrödinger equation of particles in external Gravitational Field can be compiled. The solution of Schrödinger equation demonstrates phase shift for the wave function of particles in external Gravitational Field. The phase shift from vector potential of Gravitational Field is also shown specifically in formula.
Title: Particle’s wave function equation considered scalar potential and vector potential of Gravitational Field
Description:
By the resolution of the geodesic line equation for external Gravitational Field, to get the gravitational field strength which contains scalar potential and vector potential as key parameters.
Base on the field strength, Lagrangian L for the system of particle associate with the external Gravitational Field is constituted.
Components which contribute to L are also discussed.
Thus the Hamiltonian H is derived from L meanwhile the non-relativistic Hamiltonian of the system is concluded as well.
Through the Hamiltonian H of system, Schrödinger equation of particles in external Gravitational Field can be compiled.
The solution of Schrödinger equation demonstrates phase shift for the wave function of particles in external Gravitational Field.
The phase shift from vector potential of Gravitational Field is also shown specifically in formula.
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