# Analysis of Novel Oscillations of Quantized Mechanical Energy in Mass-Accreting Nano-Oscillator Systems

## Abstract

**:**

## 1. Introduction

## 2. Preliminary Analysis in Classical Domain

## 3. Quantum Analysis

#### 3.1. Linearly Mass-Accreting Oscillator

#### 3.2. Comparison with the Exponentially Mass-Accreting Oscillator

## 4. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Quantum energy of a linearly mass-accreting oscillator with various values of k. We used ${c}_{1}={c}_{2}=1$, $m=1$, ${\omega}_{0}=1$, ${Q}_{0}=1$, and $\hslash =1$.

**Figure 2.**Detailed comparison of the quantum energy (solid red line) with the classical energy (thick dotted blue line) for linearly mass-accreting oscillator, under the limit $\hslash \to 0$ for the quantum energy. We used ${c}_{1}={c}_{2}=1$, $m=1$, $k=0.1$, ${\omega}_{0}=1$, and ${Q}_{0}=1$.

**Figure 3.**Quantum mechanical energy (solid red line), (under the limit $\hslash \to 0$), of exponentially mass-accreting oscillator given in Equation (29) with $\gamma =0.1$ for (

**A**) and $\gamma =0.5$ for (

**B**). The long dashed blue line is the corresponding kinetic energy, whereas the short dashed green line is the potential energy. A slim violet curve is the relative position of the oscillator. We used $A=1$, $m=1$, ${\omega}_{0}=1$, and $\phi =1$.

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**MDPI and ACS Style**

Choi, J.R.
Analysis of Novel Oscillations of Quantized Mechanical Energy in Mass-Accreting Nano-Oscillator Systems. *Axioms* **2021**, *10*, 153.
https://doi.org/10.3390/axioms10030153

**AMA Style**

Choi JR.
Analysis of Novel Oscillations of Quantized Mechanical Energy in Mass-Accreting Nano-Oscillator Systems. *Axioms*. 2021; 10(3):153.
https://doi.org/10.3390/axioms10030153

**Chicago/Turabian Style**

Choi, Jeong Ryeol.
2021. "Analysis of Novel Oscillations of Quantized Mechanical Energy in Mass-Accreting Nano-Oscillator Systems" *Axioms* 10, no. 3: 153.
https://doi.org/10.3390/axioms10030153