# Generalized Version of the Creation and Annihilation Operators for the Schr\"odinger Equation

## TL;DR

This paper introduces a generalized form of creation and annihilation operators for the Schrödinger equation, enabling factorization across twelve different separable coordinate systems, advancing quantum operator methods.

## Contribution

It develops a generalized version of the creation and annihilation operators and demonstrates their applicability to factorize the Schrödinger equation in multiple coordinate systems.

## Key findings

- Generalized operators enable factorization in twelve coordinate systems
- The approach extends the applicability of creation and annihilation operators
- Facilitates solving Schrödinger equation in various separable coordinates

## Abstract

A generalized version of the creation and annihilation operators is constructed and the factorization of the Schr\"odinger equation is investigated. It is shown that the generalized version of factorization operators yield a factorization for the twelve different separable coordinates for the Schr\"odinger equation.