A 2D Harmonica Oscillator For Holes In Magnetic Field


I am bemused by a sign convention for Holes, My questions are as follow:

For an electron inside the 2D Circular Quantum Well. We can write our Hamiltonian as

H = 1/2m * ( p - q A)^2 + 1/2 m w^2 r^2 (Should we use minus in the momentum term? I think for Holes, it is)

If we expand this Hamiltonian under gauge A = -B/2 (y,x,0), we will obtain a effective 2D Harmonica Oscillator with a extra term :

H = 2D-Harmonica Oscillator - w_c/2 l_z (This sign is confusing)

where l_z is the angular momentum operators in z direction.
My question is, are the two minus signs make sense in my equations?

I am not too sure if it is correct because I have seen some literature get a total different sign, And this will affect the spectrum of the hole.

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.

Want to reply to this thread?

"2D Harmonica Oscillator For Holes In Magnetic Field" You must log in or register to reply here.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Top Threads