We use the Hartree-Fock method to find the ground state energy and chemical potential of 2D quantum dots.
The many-body wavefunction is approximated by expantion into a single particle basis of harmonic oscillators via a Slater determinant. Then the Fock matrix is computed in order to solve the Roothasn equations using a self consistent field iteration. With the obtained coeficients we compute, as said, the ground state energy, the particle density and the dipole moment of the quantum dot. Having implemented this initial calculations we could potentially go further and find more properties of quantum dots such as the energy of excited states.
- Álvaro Bermejillo Seco
- Daniel Bedialauneta Rodríguez
- Marc Serra Peralta
[1] Johnson, N. F., and M. Reina. "The accuracy of the Hartree-Fock approximation for quantum dots." Journal of Physics: Condensed Matter 4.47 (1992): L623.
[2] Pfannkuche, Daniela, Vidar Gudmundsson, and Peter A. Maksym. "Comparison of a Hartree, a Hartree-Fock, and an exact treatment of quantum-dot helium." Physical Review B 47.4 (1993): 2244.
[3] Weinbub, Josef, and Robert Kosik. "Computational Perspective on Recent Advances in Quantum Electronics: From Electron Quantum Optics to Nanoelectronic Devices and Systems." Journal of Physics: Condensed Matter (2022).