diff --git a/README.md b/README.md index 40d8b60..7ab7560 100644 --- a/README.md +++ b/README.md @@ -36,27 +36,24 @@ Feel free to explore, contribute, and share your insights! 1- [Joseph Fourier](*) **(1822)**
────────────── - * 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: - - $\huge \color{DeepSkyBlue} \hat{f}(k) = \int_{-\infty}^{\infty} f(x) \, e^{-2\pi i k x} \, dx$ - -
+ **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. + +