16 Jul PHYSICS OF LOW-DIMENSIONAL SYSTEMS
hi,I’ve this assignment and I really need help with it as soon as possible.Thank you Document Preview: PHYSICS OF LOW-DIMENSIONAL SYSTEMS Problems e-e interactions- 2. Consider a 2D parabolic quantum dot with single particle Energy levels of 2 HO E(n,m)=w0 (n+m+1) Draw energy spectrum, including s and p-shell, and add (1,1) state from the d-shell Assign indices 1 to (0,0), 2 to (1,0) , 3 to (0,1), 4 to (1,1) levels The Hamiltonian for N electrons in second quantization is written as c) Write the Hartree-Fock state for N=2 electrons with Sz=0 (one up one down) Matrix elements in units of are =0.6875 =0.1875 PHYSICS OF LOW-DIMENSIONAL SYSTEMS Problems excitons-Hubbard model topology Nov28-2014 Excitons – consider a 1D system with single particle energy levels E(m)=w0*m where m=1,2,3,4 is angular momentum. Hamiltonian is given as With direct elements exchange elements a) Draw the single particle energy spectrum as a function of m. PHYSICS OF LOW-DIMENSIONAL SYSTEMS Problems excitons-Hubbard model topology Nov28-2014 b) put 2 spin up and two spin down electrons into lowest energy configuration |GS>.Write explicitly this state in terms of creation operators. Calculate total energy and express it as a sum of energy of quasiparticles. Calculate selfenergies and plot quasiparticle Energy spectrum for U=1, w0=1. c) Consider singlet and triplet excitations from |GS> with delta m=2 and delta Sz=0 (no change of spin). Picture them as electrons and holes using your single particle energy spectrum. Demonstrate explicitly that they are indeed spin singlet and triplet states by using first quantization representation. d)How many singlet and triplet excitons with delta m=2 do you find? e) Is there a bi-exciton possible? PHYSICS OF LOW-DIMENSIONAL SYSTEMS Problems excitons-Hubbard model topology Nov28-2014 f) write the Hamiltonian in the space of singlet/triplet excitons only diagonalise it and determine your excitation spectrum. g) Plot your excitation spectrum… Attachments: problems-nov2….pptx
Our website has a team of professional writers who can help you write any of your homework. They will write your papers from scratch. We also have a team of editors just to make sure all papers are of HIGH QUALITY & PLAGIARISM FREE. To make an Order you only need to click Ask A Question and we will direct you to our Order Page at WriteDemy. Then fill Our Order Form with all your assignment instructions. Select your deadline and pay for your paper. You will get it few hours before your set deadline.
Fill in all the assignment paper details that are required in the order form with the standard information being the page count, deadline, academic level and type of paper. It is advisable to have this information at hand so that you can quickly fill in the necessary information needed in the form for the essay writer to be immediately assigned to your writing project. Make payment for the custom essay order to enable us to assign a suitable writer to your order. Payments are made through Paypal on a secured billing page. Finally, sit back and relax.
About Writedemy
We are a professional paper writing website. If you have searched a question and bumped into our website just know you are in the right place to get help in your coursework. We offer HIGH QUALITY & PLAGIARISM FREE Papers.
How It Works
To make an Order you only need to click on “Order Now” and we will direct you to our Order Page. Fill Our Order Form with all your assignment instructions. Select your deadline and pay for your paper. You will get it few hours before your set deadline.
Are there Discounts?
All new clients are eligible for 20% off in their first Order. Our payment method is safe and secure.