Kindness in words creates confidence.
Kindness in thinking creates profoundness.
Kindness in giving creates love. – Lao Tzu
I read the article written by Manuel Castels a Spanish sociologist, speaking about the Spain Universities and making some social considerations on the actual role of the University in the modern era and how it should be in a modern Country.
The article has been taken from the site of the “Internazionale” a popular Italian weekly magazine reporting articles taken from foreign journals and magazines.
Quantum effects → must show an appreciable relative variation over a distance of the order of a wavelength.
Square Potentials → discontinuities of the first kind.
Schrödinger equation →
→ linear combination of imaginary exponentials:
→ linear combination of real exponentials:
The parameters of these combinations are fixed by the condition of continuity of the wavefunction and of its first derivative at the points of discontinuity of the potential.
Eingenfunction → solution bounded everywhere (at both and ).
Energy lower than the potential over the entire interval (; ) →No solutions
From D. Gatteschi, R. Sessoli, J. Villain book: Molecular Nanomagnets (2006)
The Spin Hamiltonian approach is widely used in various spectroscopies.
The Spin Hamiltonian approach eliminates all the orbital coordinates needed to describe the system and replaces them with spin coordinates, taking advantage of the symmetry properties of the system. An example of these approximations coming from the symmetry is the quencing of orbital angular momentum of the magnetic bricks.
The system with orbitally non-degenerate ground states are usually well treated with the Spin Hamiltonian approach.