Spin and Wave Function of an Elementary Particle

Yu.V. Novozhilov

Eugen Merzbacher

The requirement that the quantal wave function be single-valued is examined in the light of two recent developments: The effect of a magnetic vector potential on a particle moving in a multiply connected field-free region (Aharonov-Bohm effect), and the flux quantization inside a superconducting ring. Both of these effects are new applications of conventional elementary quantum mechanics. The single-valuedness problem is considered, with its historical background, for particles with no spin, particles with spin 12, and rigid bodies. It is shown that the single-valuedness condition, if properly adapted to the particular physical model, is deeply rooted in the foundations of quantum mechanics. However, wave functions which superficially appear to be double-valued are useful in an helicity representation of spinors and in the construction of nuclear wave functions.

Luca Salasnich

T. D. Newton, E. P. Wigner

It is attempted to formulate the properties of localized states on the basis of natural invariance requirements. Chief of these is that a state, localized at a certain point, becomes, after a translation, orthogonal to all the undisplaced states localized at that point. It is found that the required properties uniquely define the set of localized states for elementary systems of non-zero mass and arbitrary spin. The localized functions belong to a continuous spectrum of an operator which it is natural to call the position operator. This operator has automatically the property of preserving the positive energy character of the wave function to which it is applied (and it should be applied only to such wave functions). It is believed that the development here presented may have applications in the theory of elementary particles and of the collision matrix.

Diganta Parai, Nikhilesh Maity

According to symmetrization postulate for a system of identical particles, wave function has to be completely symmetric or completely anti-symmetric. In this paper we want to mathematically justify this postulate ignoring the spin part of wave function in three dimension. For a system of N identical particles, if the solution to the governing Schrodinger equation meets these criteria: a) the probability density remains invariant when any two particle positions are exchanged over time, b) the wave function is continuous and has a continuous gradient, and the system exhibits the following characteristics: c) the configuration space, which is 3N dimensional, is connected, and d) the potential term in the Hamiltonian is invariant under the exchange of any two particle positions, then the wave function must be either totally symmetric or totally antisymmetric over time.

Y. N. Kim