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Update README.md
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README.md

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@@ -36,27 +36,24 @@ Feel free to explore, contribute, and share your insights!
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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.
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* Developed the mathematical framework for the Fourier Transform, which is foundational in quantum mechanics and quantum computing.
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Formula for Fourier Transform:
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$\huge \color{DeepSkyBlue} \hat{f}(k) = \int_{-\infty}^{\infty} f(x) \, e^{-2\pi i k x} \, dx$
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<br>
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**Formula for Fourier Transform:**
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$$\hat{f}(k) = \int_{-\infty}^{\infty} f(x) \, e^{-2\pi i k x} \, dx$$
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Formula for Inverse Fourier Transform:
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$f(x) = \int_{-\infty}^{\infty} \hat{f}(k) \, e^{2\pi i k x} \, dk$
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**Formula for Inverse Fourier Transform:**
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$$f(x) = \int_{-\infty}^{\infty} \hat{f}(k) \, e^{2\pi i k x} \, dk$$
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Where:
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- $large \color{DeepSkyBlue} f(x)$ is the original function in the spatial domain.
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- $large \color{DeepSkyBlue} \hat{f}(k)$ is the transformed function in the frequency domain.
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- $large \color{DeepSkyBlue} x$ represents position, and $k$ represents momentum or frequency.
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- $f(x)$ is the original function in the spatial domain.
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- $\hat{f}(k)$ is the transformed function in the frequency domain.
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- $x$ represents position, and $k$ represents momentum or frequency.
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**Relevance in Quantum Mechanics and Computing:**
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- **Quantum Mechanics**: Converts wavefunctions between position and momentum spaces.
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- **Quantum Computing**: Basis for the Quantum Fourier Transform (QFT), essential for algorithms like Shor's factoring algorithm.
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- **Quantum Mechanics**: Converts wavefunctions between position and momentum spaces.
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- **Quantum Computing**: Basis for the Quantum Fourier Transform (QFT), essential for algorithms like Shor's factoring algorithm.
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<br><br>

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