Planck scale physics of the single-particle Schrödinger equation with gravitational self-interaction

Pramana

Vikram Soni¹ 

[1] National Physical Laboratory, K.S. Krishnan Marg, New Delhi 110 016, India$$

关键词: Quantum mechanics;    gravitation;    state reduction.;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

We consider the modification of a single-particle Schrödinger equation by the inclusion of an additional gravitational self-potential term which follows from the prescription that the ‘mass-density’ that enters this term is given by $m|Psi(overrightarrow{r}; t)|^{2}$, where $Psi(overrightarrow{r}; t)$ is the wave function and 𝑚 is the mass of the particle. This leads to a nonlinear equation, the ‘Newton–Schrödinger’ equation, which has been found to possess stationary self-bound solutions, whose energy can be determined using an asymptotic method. We find that such a particle strongly violates the superposition principle and becomes a black hole as its mass approaches the Planck mass.

【 授权许可】

Unknown