Momentum term to be expanded in dirac gamma matrices

help1please
Messages
167
Reaction score
0

Homework Statement



I need help to expand some matrices

Homework Equations



\pi = \frac{\partial \mathcal{L}}{\partial \dot{q}} = i \hbar \gamma^0

The Attempt at a Solution



How do I expand

i\hbar \gamma^0

the matrix in this term, I am a bit lost. All the help would be appreciated!
 
Physics news on Phys.org
help1please said:

Homework Statement



I need help to expand some matrices

Homework Equations



\pi = \frac{\partial \mathcal{L}}{\partial \dot{q}} = i \hbar \gamma^0

The Attempt at a Solution



How do I expand

i\hbar \gamma^0

the matrix in this term, I am a bit lost. All the help would be appreciated!


Can no one answer my question?
 
help1please said:
\pi = \frac{\partial \mathcal{L}}{\partial \dot{q}} = i \hbar \gamma^0

That looks odd. Can you give us the Lagrangian that you're starting with?
 
TSny said:
That looks odd. Can you give us the Lagrangian that you're starting with?

It has been a while since I dabbled with Dirac matrices... factoring gamma zero is simply 1.


DUH to me.
 
Thread 'Need help understanding this figure on energy levels'
This figure is from "Introduction to Quantum Mechanics" by Griffiths (3rd edition). It is available to download. It is from page 142. I am hoping the usual people on this site will give me a hand understanding what is going on in the figure. After the equation (4.50) it says "It is customary to introduce the principal quantum number, ##n##, which simply orders the allowed energies, starting with 1 for the ground state. (see the figure)" I still don't understand the figure :( Here is...
Thread 'Understanding how to "tack on" the time wiggle factor'
The last problem I posted on QM made it into advanced homework help, that is why I am putting it here. I am sorry for any hassle imposed on the moderators by myself. Part (a) is quite easy. We get $$\sigma_1 = 2\lambda, \mathbf{v}_1 = \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} \sigma_2 = \lambda, \mathbf{v}_2 = \begin{pmatrix} 1/\sqrt{2} \\ 1/\sqrt{2} \\ 0 \end{pmatrix} \sigma_3 = -\lambda, \mathbf{v}_3 = \begin{pmatrix} 1/\sqrt{2} \\ -1/\sqrt{2} \\ 0 \end{pmatrix} $$ There are two ways...
Back
Top