# Quantum Ground State Energies for Very Flat Potentials

## TL;DR

This paper develops an approximate method to calculate ground state energies for a sequence of flat potential wells, accurately matching the harmonic case and providing intuitive energy partitioning.

## Contribution

It introduces a new approximate expression for ground state energies applicable to various potential wells, including the harmonic potential, with a clear energy partitioning interpretation.

## Key findings

- Exact for harmonic potential
- Intuitively correct for all potentials
- Provides a partitioned energy expression

## Abstract

An infinite sequence of potential well functions is considered. A trial wavefunction is used with the Schr$\ddot{\text{o}}$dinger equation to obtain an approximate ground state energy for each potential well function. We obtain an expression that is exactly correct for the harmonic potential, has an intuitively correct form for all of our potential well functions and can be understood to be a partitioning of the ground state energy into two parts, one kinetic and one potential.