QM - Spin operator conjugate question

In summary, The question is about matrices and the user is trying to determine if Psi* is a 1x2 matrix with 'i's turned to '-i's. They provide an image with the question and the attempt at a solution, but are unsure of what they did wrong. You suggest multiplying the 2x2 matrix of Sx with the state v, then multiplying the resulting 2x2 matrix with the conjugate of v. The user clarifies that v is a 2x1 matrix and when they multiply Sx with v, they get a 2x1 matrix instead of a 2x2.
  • #1
QMQuestions2
2
0

Homework Statement



Okay so I've got a question I really need answered first up! If I have a 2x1 matrix for Psi, is Psi* a 1x2 matrix with all the 'i's turned to '-i's?

Now onto the actual question - http://imgur.com/3ucb4" [Broken] - part b only

Homework Equations



http://imgur.com/bcEm3" [Broken]

(Sorry to URL everything)

The Attempt at a Solution



http://imgur.com/FW0dP" [Broken]

What did I do wrong?
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
Simply have the 2 x 2 matrix of Sx operate on the state v, then multiply your new 2 x 2 matrix with the conjugate of v.

And yes the conjugate of v is a transpose matrix with the i's all different.
 
  • #3
Isn't that what I did? v is a 2x1 matrix. When I multiply Sx with v I'm left with a 2x1 matrix, not a 2x2.

Sx times v = v

v* times v = 2

Integral = infinity
 

1. What is a spin operator in quantum mechanics?

The spin operator in quantum mechanics is a mathematical operator that describes the intrinsic angular momentum of particles. It is represented by the symbol S and has eigenvalues that correspond to the possible spin states of a particle.

2. What does it mean for a spin operator to be conjugate?

In quantum mechanics, conjugate operators are operators whose commutator (a mathematical operation) is equal to the identity operator. This means that they have well-defined and complementary properties and can be used to determine the values of different physical quantities.

3. How is the spin operator used in quantum mechanics?

The spin operator is used to describe the spin state of a particle. It is often used in conjunction with other operators, such as the position and momentum operators, to determine the overall state of a quantum system.

4. Can the spin operator be measured?

Yes, the spin operator can be measured experimentally. The measurement of the spin operator results in an eigenvalue, which corresponds to the spin state of the particle being measured.

5. What are the possible eigenvalues of the spin operator?

The possible eigenvalues of the spin operator depend on the spin quantum number of the particle being measured. For spin 1/2 particles, the eigenvalues are +1/2 and -1/2, while for spin 1 particles, the eigenvalues are +1, 0, and -1.

Similar threads

  • Advanced Physics Homework Help
Replies
1
Views
208
  • Advanced Physics Homework Help
Replies
1
Views
1K
  • Advanced Physics Homework Help
Replies
1
Views
5K
  • Advanced Physics Homework Help
Replies
1
Views
794
  • Advanced Physics Homework Help
Replies
1
Views
1K
  • Advanced Physics Homework Help
Replies
14
Views
2K
  • Advanced Physics Homework Help
Replies
3
Views
2K
  • Advanced Physics Homework Help
Replies
3
Views
2K
  • Advanced Physics Homework Help
Replies
9
Views
1K
  • Advanced Physics Homework Help
Replies
5
Views
2K
Back
Top