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cgw
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I am not quite clear on the use of Fourier series to solve the Schrodinger equation.
Can you point me to a source of some simple one dimensional examples?
Can you point me to a source of some simple one dimensional examples?
A Fourier series is a way to represent a periodic function as a sum of sine and cosine functions with different amplitudes and frequencies. It is named after French mathematician Joseph Fourier and is used in many areas of science and engineering to analyze and approximate complex periodic functions.
Fourier series are used in many fields of science, including physics, engineering, and signal processing. They can be used to analyze and approximate periodic phenomena such as sound waves, electromagnetic waves, and vibrations. They are also used in image processing and data compression.
Understanding the application of Fourier series is important because it allows scientists and engineers to accurately analyze and approximate complex periodic functions. This can lead to advancements in various fields, such as telecommunications, audio and video processing, and medical imaging.
One challenge in applying Fourier series is choosing an appropriate number of terms to include in the series in order to accurately represent the periodic function. Another challenge is dealing with functions that are not strictly periodic, which may require the use of more advanced techniques such as Fourier transforms.
No, Fourier series are only applicable to periodic functions. However, there are extensions of Fourier series, such as the Fourier transform, that can be used to analyze non-periodic functions. These techniques are commonly used in fields such as image and signal processing.