Orbit track of electron's motion in constant magnetic field studied via | λ〉 representation

• Published in: Physics letters. A Vol. 267; no. 2; pp. 194 - 200
• Main Authors: Fan, Hong-Yi, Lin, Jing-Xian
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 13.03.2000
• ISSN: 0375-9601; 1873-2429
• DOI: 10.1016/S0375-9601(00)00045-1

We find that in | λ〉 representation, |λ〉= exp − |λ| 2 2 −iλΠ ++λ ∗K ++iΠ +K + |00〉 , the Hamiltonian H=(Π +Π −+ 1 2 )Ω of an electron in uniform magnetic field displays its differential operation form naturally and directly, and the Landau state with definite energy n and angular momentum number m l can be identified as | n, n− m l 〉 in the Fock space spanned by ( Π +, K +), where K += MΩ 2 (x 0−iy 0) , ( x 0, y 0) is the guiding center. Based on this the orbit track and the variance of ( x 0, y 0) as well as its squeezing effect are analysed.