# Analytic treatment of IR-spectroscopy data for double well potential

## TL;DR

This paper introduces a theoretical method using exact solutions of the Schrödinger equation for analyzing IR spectroscopy data of particles in a double well potential, enabling precise modeling of hydrogen bonds.

## Contribution

It presents a novel analytical approach leveraging special functions for efficient and accurate energy level calculations in double well potentials, applicable to experimental IR data analysis.

## Key findings

- Accurate energy spectrum calculations for hydrogen bonds in CrOOH and KDP.
- Method aligns well with experimental IR spectroscopy data.
- Simplifies analysis using Mathematica's special functions.

## Abstract

A theoretical scheme for the analysis of experimental data on IR spectroscopy for a quantum particle in a double well potential (DWP) is suggested. The analysis is based on the trigonometric DWP for which the exact analytic solution of the Schr\"odinger equation is available. The corresponding energy levels along with their wave functions are expressed via special functions implemented in {\sl {Mathematica}} (spheroidal function and its spectrum of eigenvalues). As a result trigonometric DWP makes the calculation of the energy levels an extremely easy procedure. It contains three parameters allowing one to model the most important characteristics of DWP (barrier height and the distance between the minima of the potential) along with the required asymmetry. Our approach provides an accurate calculation of the energy spectrum for hydrogen bonds in chromous acid (CrOOH) and potassium dihydrogen phosphate (${\rm{KH_2PO_4}}$) along with their polarizability in agreement with available experimental data.