# Fourier Transform of a Square Wave

A square pulse of height H extends from . Find its Fourier transform.

The given function is called a "rectangle function" and it is defined as x(t)= H* rect(t/A). This function is also called the "unit gate function".

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#### Solution Preview

A square pulse of height H extends from . Find its Fourier transform.

SOLUTION:

STEP 1: The given function is called a "rectangle function" and it is defined as x(t)= H* rect(t/A). This function is also called the "unit gate function".

STEP 2: Find the Fourier transform of ...

#### Solution Summary

The solution provides a step-by-step solution to determine the Fourier transform of the square wave using integrals.

Momentum Representation, Momentum Space Wave Function

We study the relationship between the position space wave function and the momentum space wave function in quantum mechanics. We show that they are related by the Fourier transform, more specifically we show that a momentum wave function given by the Fourier transform of the space wave function satisfies the requirements to be a momentum wave function, that is, normalization (the integral of its magnitude square equals one) and gives the correct formula for the expected value of the momentum.

See the attached file.

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