Stern Gerlach Experiment, bra(c)kets etc

In summary, the individual is new to quantum physics and is currently studying various topics such as the Schrödinger equation, infinite square well, hydrogen atom, angular momentum, and the Stern-Gerlach experiment. They are also learning about Dirac's bra-ket formalism and the importance of using kets, bras, and operators in terms of vectors spaces in quantum physics. The significance of these concepts is not yet clear, but the individual is continuing to study and learn about them. The textbook by Sakurai is recommended for a better understanding of quantum theory.
  • #1
bugatti79
794
1
Hi all,

This is my first post to the physics forum. I am completely new to quantum physics and have just gone through lecture notes on the Schrödinger equation, infinite square well, hydrogen atom and angular momentum etc.
I am currently starting on the Stern-Gerlach experiment, bras and kets via Sakurai’s Modern Quantum mechanics book. In general terms,

• Why do we have to use kets, bras and operators (Vectors Spaces) and for what?
• What’s their significance both mathematically and physically?
I suspect that as I study it further it might become clearer but at the moment I am going in blind.

Thanks
 
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  • #2
Dirac's bra-ket formalism is first of all an ingenious invention of a very helpful notation.

Also one should emphasize that quantum theory is not well understood, if one thinks in terms of wave mechanics only about it, and older textbooks overemphasize the wave-function approach. A full understanding of quantum theory can imho only be reached when learning the abstract formalism in terms of the abstract Hilbert-space formalism. The textbook by Sakurai is excellent. So just go ahead!
 
  • #3
Ok Thanks
 

Related to Stern Gerlach Experiment, bra(c)kets etc

What is the Stern Gerlach Experiment?

The Stern Gerlach Experiment is a famous experiment in quantum mechanics that was carried out in 1922 by Otto Stern and Walther Gerlach. It demonstrated the existence of electron spin and the quantization of angular momentum, which helped to confirm the principles of quantum mechanics.

How does the Stern Gerlach Experiment work?

In the experiment, a beam of silver atoms is passed through an inhomogeneous magnetic field. The atoms are deflected either up or down depending on the orientation of their electron spin, which is either parallel or antiparallel to the magnetic field. This results in two distinct beams of atoms, which can be observed on a detector plate.

What are bra(c)kets in quantum mechanics?

Bra(c)kets are a mathematical notation used in quantum mechanics to represent quantum states. The "bra" | \langle \psi | represents the complex conjugate of a quantum state, while the "ket" | \psi \rangle represents the quantum state itself. The inner product of a bra and a ket \langle \phi | \psi \rangle gives the probability amplitude for the state |\psi\rangle to collapse into the state |\phi\rangle upon measurement.

What is the significance of the Stern Gerlach Experiment in quantum mechanics?

The Stern Gerlach Experiment is significant because it provided evidence for the quantization of angular momentum and the existence of electron spin, both of which are fundamental principles of quantum mechanics. It also demonstrated the probabilistic nature of quantum systems and the importance of measurement in determining the properties of a system.

What are some applications of the Stern Gerlach Experiment?

The Stern Gerlach Experiment has been used in various applications, such as testing the validity of quantum mechanics, studying the properties of spin states in atoms and molecules, and developing technologies such as quantum computing. It has also been used to investigate fundamental questions about the nature of reality and the role of measurement in quantum systems.

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