@@ -36,27 +36,24 @@ Feel free to explore, contribute, and share your insights!
3636
37371- [ Joseph Fourier] ( * ) ** (1822)** <br >
3838 ──────────────
39- * Developed the mathematical framework for the Fourier Transform, which is foundational in quantum mechanics and quantum computing.
39+ * Developed the mathematical framework for the Fourier Transform, which is foundational in quantum mechanics and quantum computing.
4040
41- Formula for Fourier Transform:
42-
43- $\huge \color{DeepSkyBlue} \hat{f}(k) = \int_ {-\infty}^{\infty} f(x) \, e^{-2\pi i k x} \, dx$
44-
45- <br >
41+ ** Formula for Fourier Transform:**
42+ $$ \hat{f}(k) = \int_{-\infty}^{\infty} f(x) \, e^{-2\pi i k x} \, dx $$
4643
47- Formula for Inverse Fourier Transform:
48-
49- $f(x) = \int_ {-\infty}^{\infty} \hat{f}(k) \, e^{2\pi i k x} \, dk$
44+ ** Formula for Inverse Fourier Transform:**
45+ $$ f(x) = \int_{-\infty}^{\infty} \hat{f}(k) \, e^{2\pi i k x} \, dk $$
5046
5147 Where:
52- - $large \color{DeepSkyBlue} f(x)$ is the original function in the spatial domain.
53- - $large \color{DeepSkyBlue} \hat{f}(k)$ is the transformed function in the frequency domain.
54- - $large \color{DeepSkyBlue} x$ represents position, and $k$ represents momentum or frequency.
48+ - $f(x)$ is the original function in the spatial domain.
49+ - $\hat{f}(k)$ is the transformed function in the frequency domain.
50+ - $x$ represents position, and $k$ represents momentum or frequency.
5551
56-
5752 ** Relevance in Quantum Mechanics and Computing:**
58- - ** Quantum Mechanics** : Converts wavefunctions between position and momentum spaces.
59- - ** Quantum Computing** : Basis for the Quantum Fourier Transform (QFT), essential for algorithms like Shor's factoring algorithm.
53+ - ** Quantum Mechanics** : Converts wavefunctions between position and momentum spaces.
54+ - ** Quantum Computing** : Basis for the Quantum Fourier Transform (QFT), essential for algorithms like Shor's factoring algorithm.
55+
56+
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6259<br ><br >
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