# The relations between d-dimensional isotropic oscillator and D-dimensional like-hydrogen atom

## TL;DR

This paper establishes a mathematical relationship between d-dimensional isotropic oscillators and D-dimensional like-hydrogen atoms, enabling the transfer of solutions and properties across different quantum systems and dimensions.

## Contribution

It introduces a special transformation that relates Schrödinger equations of different dimensions for these systems, generalizing solutions between isotropic oscillators and like-hydrogen atoms.

## Key findings

- Derived a transformation linking quantum systems in different dimensions.
- Generalized energy spectra and wave functions across dimensions.
- Provided a method to solve hydrogen-like problems using oscillator solutions.

## Abstract

Being comparable in quantum systems makes it possible for spaces with varying dimensions to attribute each other using special conversions can attribute schrodinger equation with like-hydrogen atom potential in defined dimensions to a schrodinger equation with other certified dimensions with isotropic oscillator potential. Applying special transformation provides a relationship between different dimensions of two quantum systems. The result of the quantized isotropic oscillator can be generalized to like-hydrogen atom problem in different dimensions. The connection between coordinate spaces in different dimensions can follow a specific relation that by using it and applying the parametric definition in two problems, energy spectrum and like-hydrogen atom potential wave functions problem will be solved.