exercise set: 1. (a) Write down the Dirac Hamiltonian by taking a Legendre transformation of Dirac Lagrangian. (b) Show that the generator of rotation (which is angular momentum operator) doesn't commute with the Hamiltonian. (c) Write down explicit version of alpha i tilda matrix and take commutation of it with alpha j (d) Again take commutation of alpha i tilda with beta matrix (e) Calculate the [ ᾰi , H ] . Use results you've found in previous questions. 2. (a) Derive the conjugate Dirac spinor. (b) Write down the conjugate Dirac equation. (c) By using them, calculate the continuity equation for Dirac spinor.
it's a model, so it is imagination. but that's not what you meant... this theory will be modified to a field theory in some of the next lectures. And the interpretation will be very different. But in semiconductors the idea of these holes is applied quite literally.
That doesnt make any sense, we invented some random gamma matrices and developed an idea of a new Hamiltonian, then found out that it doesnt commute with the angular momentum, as we would expect. Therefore there is something missing? Seems like a lot of ad hoc stuff.
exercise set:
1. (a) Write down the Dirac Hamiltonian by taking a Legendre transformation of Dirac Lagrangian.
(b) Show that the generator of rotation (which is angular momentum operator) doesn't commute with the Hamiltonian.
(c) Write down explicit version of alpha i tilda matrix and take commutation of it with alpha j
(d) Again take commutation of alpha i tilda with beta matrix
(e) Calculate the [ ᾰi , H ] . Use results you've found in previous questions.
2. (a) Derive the conjugate Dirac spinor.
(b) Write down the conjugate Dirac equation.
(c) By using them, calculate the continuity equation for Dirac spinor.
Note : I just dropped this comment so that I can come here later on and check my own comprehension before exam or nothing special.
awesome!
If you have the solution for schrodinger equation for woods Saxon potential please share it with me , becuase it's important in unclear physics
I'm afraid I haven't encountred it :(
thank u..
Thank you , is dirac hole theory correct or just imagination ?
it's a model, so it is imagination.
but that's not what you meant... this theory will be modified to a field theory in some of the next lectures. And the interpretation will be very different. But in semiconductors the idea of these holes is applied quite literally.
That doesnt make any sense, we invented some random gamma matrices and developed an idea of a new Hamiltonian, then found out that it doesnt commute with the angular momentum, as we would expect. Therefore there is something missing? Seems like a lot of ad hoc stuff.