Spin vector and operator transformations query

In summary, The individual is struggling to understand spin transformations and has used Sakurai's method of changing basis vectors to transform the operator. They expected to get Sz' = Sy, but instead got Sx. They then tried using Sz' = U Sz Udagger and got the expected result of Sz'=Sy, but are confused as to why the first arrangement is considered the correct form according to their texts. They are seeking help with this confusion.
  • #1
deneve
37
0
I am struggling to understand spin transformations and have used Sakurai's method of
|new basis> = U |old basis> to change basis vectors and hence should have

Sz' = Udagger Sz U

to transform the operator. I thought this should give Sz' = Sy in the workings (see attachment below) but it gives Sx instead. If I use
Sz' = U Sz Udagger then I do get Sz'=Sy but according to the texts I have, the first arrangement is the correct form. So I'm really confused. Can anyone see what I'm doing wrong here.


2. Homework Equations

I would be really grateful for any help with this. Thank you
 

Attachments

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  • #2
. 3. The Attempt at a Solution (The attachments are not letting me paste the math here so I have posted the link to my calculation instead). My Calculation: https://ibb.co/n6nC9x
 

1. What is a spin vector?

A spin vector is a mathematical representation of the spin of a particle. It is a vector quantity that describes the direction of the spin of a particle in three-dimensional space.

2. What is a spin operator?

A spin operator is a mathematical operator used to describe the behavior of spin in quantum mechanics. It acts on the spin vector to produce a new spin vector.

3. How do spin vectors and operators transform?

Spin vectors and operators transform according to the principles of quantum mechanics. The transformation depends on the specific scenario and can be described using mathematical equations.

4. What is the significance of spin vector and operator transformations?

Spin vector and operator transformations are important in understanding the behavior of particles at the quantum level. They allow us to predict the outcomes of experiments and understand the nature of spin in quantum mechanics.

5. How are spin vector and operator transformations applied in real-world scenarios?

Spin vector and operator transformations have many practical applications in fields such as nuclear physics, quantum computing, and magnetic resonance imaging. They are used to analyze and manipulate the spin of particles and atoms, leading to advancements in technology and scientific understanding.

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