Good introduction for dirac notation

In summary, the conversation discusses a theoretical physics paper that requires knowledge of Dirac notation. The participants suggest various resources for understanding and working with Dirac notation, including the book "Modern Quantum Mechanics" by Sakurai and the introduction in the first chapter of "Principles of Quantum Mechanics" by Shankar. It is also recommended to study mathematics, specifically linear algebra, for a deeper understanding of Dirac notation.
  • #1
Genericcoder
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Hi guys,
I m reading some theoretical physics paper that requires knowledge of dirac notation if someone could point me out to a good tutorial on it I come from a math background but I am studying this paper with my supervisor.
 
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  • #2
If you have already studied some QM (i.e have come across the SE and so on) I would recommend Modern Quantum Mechanics by Sakurai.
It is NOT a good book for absolute beginners, but then I don't think Dirac notation is usually covered in books for beginners (e.g. Griffith)
 
  • #3
I always liked the introduction by Shankar in the first chapter of his book ("Principles of Quantum Mechanics"). It requires very little prior knowledge and is quite pedagogical.
 
  • #4
The above replies are excellent if you want to get used to Dirac notation and if you want to be able to work with it. However, if you want to understand what it really is, then you will need to study some mathematics. I suggest the excellent free book "linear algebra done wrong": http://www.math.brown.edu/~treil/papers/LADW/LADW.html This will give you a good start. For ever more understanding, you will need functional analysis, but that might be overkill.
 
  • #5
Thanks a lot for the replies guys
 

1. What is Dirac notation?

Dirac notation, also known as bra-ket notation, is a mathematical notation used in quantum mechanics to represent the state of a quantum system. It was developed by physicist Paul Dirac in the 1930s and has become an essential tool for understanding and solving problems in quantum mechanics.

2. Why is Dirac notation useful?

Dirac notation is useful because it allows for a concise and elegant representation of quantum states and operations. It simplifies calculations and makes it easier to describe complex quantum systems, such as those with multiple particles and interactions.

3. What are the elements of Dirac notation?

The two main elements of Dirac notation are the bra and ket vectors, represented by the symbols < and | respectively. The bra vector <A| represents the dual vector to the ket |A>, and together they form a complete set of basis vectors that can describe any quantum state.

4. How are bra and ket vectors related?

Bra and ket vectors are related by the complex conjugate operation. The bra vector <A| is the complex conjugate transpose of the ket vector |A>. This means that the elements of the bra vector are the complex conjugates of the elements of the ket vector.

5. Can Dirac notation be applied to classical systems?

No, Dirac notation is specific to quantum mechanics and cannot be applied to classical systems. It is based on the principles of superposition and entanglement, which are unique to quantum mechanics and do not apply to classical systems.

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