# An Asymmetric Model Position Dependent Mass: Quantum Mechanical Study

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{3}molecule has been explained by using the PDM of the form [16]

## 2. Characteristic Features of New Asymmetric PDM

## 3. Quantum Mechanical Study on the New PDM Systems

## 4. Effect of Potential

#### 4.1. Single Well Potential

#### 4.2. Double Well Potential

#### 4.3. Gaussian Single Well Potential

#### 4.4. Rath Triangular Potential

## 5. Validity of Uncertainty Relation

## 6. Discussion and Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Phase portrait of the PDM Hamiltonian associated with single well potential for $\lambda $ = 0.01.

**Figure 5.**Phase portrait of the PDM Hamiltonian associated with single well potential for $\lambda $ = 0.1.

**Figure 6.**Energy eigenvalues of the PDM Hamiltonian associated with single potential for $\lambda =0.01$.

**Figure 8.**Phase portrait of the PDM Hamiltonian associated with double well potential for $\lambda $ = 0.01.

**Figure 9.**Phase portrait of the PDM Hamiltonian associated with double well potential for $\lambda $ = 0.1.

**Figure 10.**Energy eigenvalues of the PDM Hamiltonian associated with double well potential for $\lambda =0.01$.

**Figure 12.**Phase portrait of the PDM Hamiltonian associated with Gaussian single well type potential for (

**a**) $\lambda $ = 0.01 and (

**b**) $\lambda $ = 0.1.

**Figure 13.**Energy eigenvalues of the PDM Hamiltonian associated with Gaussian single well type potential for $\lambda =0.01$.

**Figure 15.**Phase portrait of the PDM Hamiltonian associated with Rath potential for (

**a**) $\lambda $ = 0.01 and (

**b**) $\lambda $ = 0.1.

**Figure 16.**Energy eigenvalues of the PDM Hamiltonian associated with Rath potential for $\lambda =0.01$.

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**MDPI and ACS Style**

Rath, B.; Mallick, P.; Asad, J.; Wannan, R.; Jarrar, R.; Shanak, H. An Asymmetric Model Position Dependent Mass: Quantum Mechanical Study. *Axioms* **2023**, *12*, 318.
https://doi.org/10.3390/axioms12040318

**AMA Style**

Rath B, Mallick P, Asad J, Wannan R, Jarrar R, Shanak H. An Asymmetric Model Position Dependent Mass: Quantum Mechanical Study. *Axioms*. 2023; 12(4):318.
https://doi.org/10.3390/axioms12040318

**Chicago/Turabian Style**

Rath, Biswanath, Pravanjan Mallick, Jihad Asad, Rania Wannan, Rabab Jarrar, and Hussein Shanak. 2023. "An Asymmetric Model Position Dependent Mass: Quantum Mechanical Study" *Axioms* 12, no. 4: 318.
https://doi.org/10.3390/axioms12040318