Quantum study of the spin inversion

Abstract

Spin motion is studied by means of the direct use of the Schrödinger equation. The solution is found in terms of Lommel’s polynomials. An expression of the tunneling splitting is obtained, in good agreement with the results coming from other calculations.

Inversion time of large spins

“…3, for a typical value of N ϳ 10-20, is remarkable. 3, for a typical value of N ϳ 10-20, is remarkable.…”

“…3, a full investigation taking into account the energy differences leads to the Laplace transform of Lommel's polynomials, and work is in progress in this direction. As indicated in Ref.…”

“…In particular, if Mössbauer spectroscopy is used, the inversion time of the spin is one of the most important parameters in the structure of the experimental spectra. 3 the coefficient ͉b n ͑t͉͒ 2 , which gives the probability of finding the system in the nth spin state, has been calculated and it is found to be a somewhat involute trigonometric sum. Thus, the nuclear energy levels are modified and we are in the presence of the "Mössbauer relaxation spectrum," with a structure that depends on the frequency of the inversion.…”

“…1 In a pictorial, intuitive description, as the total electronic spin of the surrounding neighbors inverts its direction, the magnetic field on the iron nucleus also changes. 3. 2 In Ref.…”

“…3, with a single Bessel function, is improved significantly. 3, with a single Bessel function, is improved significantly.…”