How to switch between momentum/real space

[Sasuke]

I'm a bit confused about using momentum and real space and switching between them and some crap about Fourier series. Can someone provide some links to where i can study these. Please keep in mind that i am new to quantum physics.

 

[Edgardo]

Check out these excellent quantum mechanics lectures:
http://www.youtube.com/view_play_list?p=0F530F3BAF8C6FCC"
Have a look at lectures 7 and 8.

http://www.youtube.com/view_play_list?p=84C10A9CB1D13841"
Have a look at lecture 5.

Depending on your knowledge you can of course watch previous lectures.

 

[Entropia]

Switching between momentum and real space is a fundamental concept in quantum physics. It involves using Fourier series to represent a wave function in terms of either momentum or position space. The choice of which representation to use depends on the physical problem at hand and the convenience of the representation.

In quantum mechanics, momentum and position are complementary variables, meaning that the more precisely we know one, the less precisely we know the other. This is known as the Heisenberg uncertainty principle. Therefore, it is often necessary to switch between the two representations in order to fully understand the behavior of a quantum system.

To switch between momentum and real space, one can use the Fourier transform, which is a mathematical tool that allows us to convert a function from one representation to another. This is achieved by decomposing the original function into a series of sinusoidal functions with different frequencies and amplitudes.

If you are new to quantum physics, it is important to have a solid understanding of Fourier series and transforms. There are many resources available online that can help you learn these concepts, such as textbooks, lecture notes, and video tutorials. Here are a few links that can provide a good introduction to Fourier series and transforms:

1. Khan Academy: This website offers a series of video tutorials on Fourier series and transforms, starting from the basics and gradually building up to more advanced concepts.

2. MIT OpenCourseWare: This is a free online platform that offers lecture notes, assignments, and video lectures on various topics, including Fourier series and transforms.

3. Quantum Mechanics for Scientists and Engineers by David Miller: This textbook provides a comprehensive introduction to quantum mechanics, including a chapter on Fourier series and transforms.

Remember that learning quantum physics takes time and effort, so don't get discouraged if you don't understand everything right away. Keep practicing and seeking out resources, and you will gradually develop a better understanding of switching between momentum and real space.