Elementary Mechanics

Elementary Quantum Mechanics

This is the first graduate course on elementary quantum mechanics in Internet written for the benefit of undergraduate and graduate students. It is a translation (with corrections) of the Romanian version of the course, which I did at the suggestion of several students from different countries. The topics included refer to the postulates of quantum mechanics, one-dimensional barriers and wells,...

Total time derivatives of operators in elementary quantum mechanics

Non-extensive statistical mechanics and particle spectra in elementary interactions

We generalize Hagedorn’s statistical theory of momentum spectra of particles produced in high-energy collisions using Tsallis’ formalism of non-extensive statistical mechanics. Suitable non-extensive grand canonical partition functions are introduced for both fermions and bosons. Average occupation numbers and moments of transverse momenta are evaluated in an analytic way. We analyse the energy...

Quantum vs Classical Mechanics : role of elementary excitations

Simple theorems relating a quantum mechanical system to the corresponding classical one at equilibrium and connecting the quantum eigenvalues to the frequencies of normal modes oscillations are presented. Corresponding to each quantum eigenfunction, a ‘classical eigenfunction’ is associated. Those belonging to ‘elementary excitations’ play an important role.

Demonstration of the spin-statistics connection in elementary quantum mechanics

The spin-statistics connection is proved using the methods of elementary quantum mechanics. The effect of exchange and space inversion operators on two-particle states is reviewed. The connection follows directly from successive application of these operations to the wave function for two identical particles in an s-state, evaluated at positions ±x, but at equal time.