diff --git a/README.md b/README.md index 4d0a5af..9f35635 100644 --- a/README.md +++ b/README.md @@ -38,24 +38,24 @@ Feel free to explore, contribute, and share your insights! ────────────── * Developed the mathematical framework for the Fourier Transform, which is foundational in quantum mechanics and quantum computing. - **Formula for Fourier Transform:** + Formula for Fourier Transform: $\huge \color{DeepSkyBlue} \hat{f}(k) = \int_{-\infty}^{\infty} f(x) \, e^{-2\pi i k x} \, dx$
- **Formula for Inverse Fourier Transform:** + 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. + - $large \color{DeepSkyBlue} f(x)$ 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. **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.