# Is the Expectation Value of the y-Component of Spin Represented by Sy?

• Sekonda
The correct operator for the y-component of the electron spin on the eigenstate of Sx is <\uparrow_{x}|\hat{S}_{y}|\uparrow_{x}>. The solutions most likely meant to use the z-direction instead of the y-direction. This is a common mistake and can easily be corrected.
Sekonda
Hey,

I'm having trouble interpreting a question, as the solutions say something different... Anyways the question part d) below:

So we want to determine the expectation value of the y-component of the electron spin on the eigenstate of Sx, now I would of thought this was given by:

$$<\uparrow_{x}|\hat{S}_{y}|\uparrow_{x}>$$

However in my solutions it uses the Spin operator in the z-direction instead, I'm note exactly sure what it means by the y-component of the electron spin though I'd of thought this y-component would of been represented by the Spin operator referring to the y components i.e. Sy.

Can someone confirm this? OR tell me why I'm wrong!

Thanks,
SK

You're right. It's probably just a typo in the solutions.

## 1. What is the Expectation Value of Spin Operator?

The Expectation Value of Spin Operator is a measure of the average value that a spin operator will yield when measured over many identical experiments. It is a key concept in quantum mechanics and is used to describe the behavior of spin particles such as electrons.

## 2. How is the Expectation Value of Spin Operator calculated?

The Expectation Value of Spin Operator is calculated by taking the inner product of the quantum state with the spin operator. This is then multiplied by the complex conjugate of the quantum state and integrated over all possible values of the spin operator. This results in a single number that represents the expectation value.

## 3. What does the Expectation Value of Spin Operator tell us about a system?

The Expectation Value of Spin Operator provides information about the average value of the spin of a system. It can tell us the most likely outcome of a measurement of the spin and also provides insight into the overall behavior and properties of spin particles in the system.

## 4. How does the Expectation Value of Spin Operator relate to other quantum mechanical concepts?

The Expectation Value of Spin Operator is closely related to other important concepts in quantum mechanics such as spin states, spin operators, and spin measurements. It is also used in calculations involving spin angular momentum and spin interactions.

## 5. Can the Expectation Value of Spin Operator be negative?

Yes, the Expectation Value of Spin Operator can be negative. This occurs when the quantum state has a negative sign in front of the spin operator or when the spin operator has a negative eigenvalue. In these cases, the expectation value will be negative, indicating a more likely negative spin measurement.

Replies
1
Views
689
Replies
31
Views
3K
Replies
1
Views
2K
Replies
1
Views
1K
Replies
14
Views
2K
Replies
3
Views
1K
Replies
5
Views
2K
Replies
2
Views
4K