Wave Function in Momentum Space | Fourier Transform

What is the representation of Wave function in Momentum space, and the corresponding probability densities and expectation values?

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In quantum mechanics, the wavefunction can be represented in both position space and momentum space. The wavefunction in position space describes the probability amplitude of finding a particle at a specific location. In momentum space, the wavefunction describes the probability amplitude of a particle having a specific momentum.

This momentum space representation is obtained through a mathematical transformation, allowing physicists to analyze and understand phenomena where momentum, rather than position, is the key variable. This is particularly useful in problems involving conservation of momentum, scattering, and analyzing particle dynamics in various potential fields.

By examining the wavefunction in momentum space, we gain insights into the particle's behavior and properties related to its momentum, providing a complementary perspective to its position space representation.

00:00 Introduction
03:20 Fourier Transform
14:48 Momentum Space Representation
31:03 Problem Solving

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