Bra/Ket Notation: Learn Basics & Find Eigenvalues

[The thinker]

Hi,

I need to read up on Bra/Ket notation for my project on Bells Inequalities. I've been through the relevant sections of J.J Sakurai's Modern Quantum Mechanics but have had a lot of trouble getting it all clear in my head.

Could anyone recommend me an online resource that might help?

(My priority at the moment is just the basics, understanding how spin states are described and the probabilities/eigenvalues found in bra/ket notation)

Thanks a lot!

 

[Fredrik]

This post explains bra-ket notation. This thread might be helpful too (but read post #17 first, where I acknowledge a silly mistake I made in #2). Wikipedia is good too.

If you're trying to learn about Bell inequalities, you might like the derivation in Isham's book: 215, 216

 

[Entropia]

Hi there,

Bra/Ket notation, also known as Dirac notation, is a commonly used mathematical notation in quantum mechanics to represent quantum states and operators. It can seem confusing at first, but with practice and understanding it can become a powerful tool for solving problems in quantum mechanics.

First, let's start with the basics. The "bra" and "ket" symbols represent the two components of a vector in a complex vector space. The "bra" symbol, < , represents the dual vector or "row vector" while the "ket" symbol, | , represents the vector or "column vector". In quantum mechanics, the "bra" and "ket" symbols are used to represent the bra and ket vectors of a quantum state, respectively. For example, the quantum state of a spin-1/2 particle can be represented as |↑> or |↓>, where the arrow represents the spin direction.

Now, let's move on to eigenvalues and probabilities. In quantum mechanics, operators are used to represent physical observables, such as spin, energy, and position. The eigenvalues of an operator represent the possible values that can be measured for that observable. In bra/ket notation, the operator is represented by a "bra" and "ket" vector, and the eigenvalues are found by solving the corresponding eigenvalue equation.

To better understand bra/ket notation and its applications in quantum mechanics, I would recommend checking out the following online resources:

1. Khan Academy's video series on bra/ket notation: https://www.khanacademy.org/science...antum-numbers-and-orbitals/v/bra-ket-notation

2. MIT's OpenCourseWare on Quantum Physics I: http://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2013/lecture-notes/

3. The University of Colorado Boulder's Quantum Mechanics Interactive Simulations: http://phet.colorado.edu/en/simulation/quantum-mechanics

I hope these resources will help you in understanding the basics of bra/ket notation and finding eigenvalues in quantum mechanics. Best of luck with your project on Bell's Inequalities!