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27 changes: 12 additions & 15 deletions README.md
Original file line number Diff line number Diff line change
Expand Up @@ -36,27 +36,24 @@ Feel free to explore, contribute, and share your insights!

1- [Joseph Fourier](*) **(1822)** <br>
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* Developed the mathematical framework for the Fourier Transform, which is foundational in quantum mechanics and quantum computing.
* Developed the mathematical framework for the Fourier Transform, which is foundational in quantum mechanics and quantum computing.

Formula for Fourier Transform:

$\huge \color{DeepSkyBlue} \hat{f}(k) = \int_{-\infty}^{\infty} f(x) \, e^{-2\pi i k x} \, dx$

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**Formula for Fourier Transform:**
$$\hat{f}(k) = \int_{-\infty}^{\infty} f(x) \, e^{-2\pi i k x} \, dx$$

Formula for Inverse Fourier Transform:

$f(x) = \int_{-\infty}^{\infty} \hat{f}(k) \, e^{2\pi i k x} \, dk$
**Formula for Inverse Fourier Transform:**
$$f(x) = \int_{-\infty}^{\infty} \hat{f}(k) \, e^{2\pi i k x} \, dk$$

Where:
- $large \color{DeepSkyBlue} f(x)$ is the original function in the spatial domain.
- $large \color{DeepSkyBlue} \hat{f}(k)$ is the transformed function in the frequency domain.
- $large \color{DeepSkyBlue} x$ represents position, and $k$ represents momentum or frequency.
- $f(x)$ is the original function in the spatial domain.
- $\hat{f}(k)$ is the transformed function in the frequency domain.
- $x$ represents position, and $k$ represents momentum or frequency.


**Relevance in Quantum Mechanics and Computing:**
- **Quantum Mechanics**: Converts wavefunctions between position and momentum spaces.
- **Quantum Computing**: Basis for the Quantum Fourier Transform (QFT), essential for algorithms like Shor's factoring algorithm.
- **Quantum Mechanics**: Converts wavefunctions between position and momentum spaces.
- **Quantum Computing**: Basis for the Quantum Fourier Transform (QFT), essential for algorithms like Shor's factoring algorithm.




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