12-14 a-magnetic_effects_in_quantum _mechanics

1. Pertemuan 12 - 14 FISIKA ZAT PADAT EFEK MAGNETIK DALAM MEKANIKA KUANTUM Iwan Sugihartono, M.Si Jurusan Fisika Fakultas Matematika dan Ilmu Pengetahuan Alam

3. Two levels system 15/03/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | | cb ( t ) | 2 = cos(ω t )2 where ω is the Rabi frequency

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8. Electron in a Magnetic field 15/03/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | Quantization P change to P op and r to r op Wave function Lev_Davidovich_Landau

9. 15/03/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | is easy to check that To actually solve Schrödinger’s equation for an electron confined to a plane in a uniform perpendicular magnetic field, it is convenient to use the Landau gauge. ) . H commutes with px , so H and px have a common set of eigenstates, taking

10. Landau Levels 15/03/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | Example of quantization measurement Effects of Landau levels are only observed when the mean thermal energy is smaller than the energy level separation, , meaning low temperatures and strong magnetic fields

13. 15/03/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | Dong-In Chang, Gyong Luck Khym , Kicheon Kang, Yunchul Chung, Hu-Jong Lee, Minky Seo, Moty Heiblum, Diana Mahalu, Vladimir Umansky Nature Physics 4, 205 (2008)

14. Aharonov-Bohm Oscillations in Semiconductor Quantum Rings 15/03/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | Now an international research team from the Nijmegen High Field Magnet Laboratory (the Netherlands), the Eindhoven University of Technology (the Netherlands), the University of Antwerp (Belgium), the University of Moldova (Moldova) and the the Institute of Microelectronics in Madrid (Spain) has succeeded to detect oscillatory currents carried by single electron states in a semiconductor quantum ring. These findings were published in the journal Physical Review Letters.

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