Eigenstates of a Charged Simple Harmonic Oscillator in a Uniform Magnetic Field
Keywords:Simple Harmonic Oscillator, Uniform Magnetic field, Landau levels, Landau gauge, Energy eigenvalues and eigenfunctions
Exact eigenstates of a simple harmonic oscillator and those of a charged particle in a uniform magnetic field are well known and frequently used. In this short article we work out the exact eigenstates of a charged harmonic oscillator placed in a uniform magnetic field using a novel gauge choice for the vector potential.
L. Landau and E. Lifshitz, The classical theory of fields Volume 2 of Course of Theoretical Physics, Fourth revised English edition, Elsevier, 2013
B.H. Bransden and C.J. Joachain, Quantum Mechanics, Second Edition, Pearson Education, First Indian reprint 2004, pp 174.
Richard L. Liboff, Introduction to Quantum Mechanics, Addison Wesley, 1980.
R. Shankar, Principles of Quantum Mechanics, 2nd ed. Plenum Press, 1994.
W. Greiner, Quantum Mechanics-An introduction, Springer-Verlag, fourth edition, first Indian reprint, 2004.
N. Sethulakshmi et.al, “Magnetism in two-dimensional materials beyond graphene”,
Materials today, Vol. 27, July-August 2019, page 107-122.
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