Development of the Schrodinger equation for attosecond laser pulse interaction with Planck gas

TL;DR

This paper introduces a hyperbolic Schrödinger equation tailored for Planck-mass particles interacting with attosecond laser pulses, exploring quantum-gravitational effects and energy spectra independence for super-Planckian particles.

Contribution

It proposes a new hyperbolic Schrödinger equation for Planck-mass particles and analyzes its solutions, including gravity effects and spectral properties.

Findings

Energy spectrum is independent of particle mass for masses greater than Planck mass.

Solution for a particle in a box demonstrates unique quantum behavior at Planck scale.

Inclusion of gravity modifies the hyperbolic Schrödinger equation for Planck particles.

Abstract

The creation of the new particles by the interaction of the ultrarelativistic ions,from Large Hadron Collider(LHC), and attosecond laser pulse open new possibilities for laser physicists community .In this paper we propose the hyperbolic Schr\"odinger equation (HSE) for gas of the "classical" particles "i.e. particles with mass= Planck mass We discuss the inclusion of the gravity to the HSE The solution of the HSE for a particle in a box is obtained. It is shown that for particles with m greater than Mp the energy spectrum is independent of the mass of particle. Key words: attosecond laser pulses, Schrodinger equation, Planck particles, thermal processes