2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/21439The usual cyclotron resonance occurs at ω_c=eB/m*c which is independent of spin. The new resonances depend on spin. The new resonances occur at ω_{c\pm}=(1/2)g_{\pm}eB/m*c where (1/2)g_{\pm}= {\it l}+(1/2)\pm s/(2{\it l}+1). The energy in the centre of two new frequencies varies as the square root of the 2-dimensional electrons due to spin excess in the Gaussian model. The frequencies ω_{c\pm} are linearly proportional to the magnetic field except near crossing point where the linear combination of wave functions must be made.4 pages TeXMesoscale and Nanoscale PhysicsStatistical Mechanicstext