Free energy for harmonically bound fermions in a magnetic field

Abstract. An analytic expression is obtained for the free energy of fermions bound in an anisotropic harmonic potential in the presence of an arbitrary magnetic field, at a finite temperature. The specific heat and the magnetic moment are readily calculated. Our results consist of two parts, a steady part and an oscillatory one. The latter is similar to the well known de Haas-van Alphen oscillation, but persists in the absence of a magnetic field. Applications of our results to the nuclear shell model and surface effects of solids are briefly discussed. 1