Exact energy-eigenstates of the Coulomb-Stark Hamiltonian

TL;DR

This paper introduces an efficient numerical algorithm to compute exact energy eigenstates of a hydrogen atom in an external electric field, enabling precise analysis of electron tunneling dynamics.

Contribution

It presents an approximation-free, numerically efficient method for solving the Coulomb-Stark Hamiltonian eigenstates, advancing computational accuracy in quantum Stark problems.

Findings

Successfully computed exact eigenstates of the Coulomb-Stark Hamiltonian.

Demonstrated application by calculating the time-dependent wavefunction during electron tunneling.

Provided a new tool for precise quantum dynamics simulations in external fields.

Abstract

An approximation-free, numerically efficient algorithm is presented for the Hamiltonian eigen-states of the Stark-Hydrogen problem describing a quantum particle exposed to the central Coulomb force and a homogeneous external field. As an example of application in a state-expansion with continuous energy, we calculate the time-dependent wavefunction of an electron tunneling from a hydrogen atom suddenly exposed to an external electric field.