Approximations for the Lowest Energy Eigenstates in a Double Square Well Potential

TL;DR

This paper provides highly accurate closed-form approximations for the lowest energy eigenstates of a particle in a double square well potential, assuming a wide barrier minimizes tunneling effects.

Contribution

It introduces novel closed-form formulas for wavefunctions and energies of the ground and first excited states in a double square well potential with minimal tunneling.

Findings

Accurate approximations for ground and first excited state energies.

Closed-form expressions for wavefunctions.

Assumption of wide barrier reduces tunneling effects.

Abstract

Highly accurate closed-form approximations are given for the ground state and first excited state wavefunctions and energies for a nonrelativistic particle in a one-dimensional double square well potential with a square barrier in between (so that the potential is a sequence of five constant pieces that alternate in value from being above and below the ground state and first excited state energies), under the assumption that the barrier is sufficiently wide that the tunneling across it is very small.