8 research outputs found
Analytic representations with theta functions for systems on ℤ(d) and on .
Get PDFyesAn analytic representation with Theta functions on a torus, for systems with variables in ℤ(d),
is considered. Another analytic representation with Theta functions on a strip, for systems with
positions in a circle S and momenta in Z, is also considered. The reproducing kernel formalism for these two systems is studied. Wigner and Weyl functions in this language, are also studied
On the truncation of the harmonic oscillator wavepacket
Get PDFWe present an interesting result regarding the implication of truncating the
wavepacket of the harmonic oscillator. We show that disregarding the
non-significant tails of a function which is the superposition of
eigenfunctions of the harmonic oscillator has a remarkable consequence: namely,
there exist infinitely many different superpositions giving rise to the same
function on the interval. Uniqueness, in the case of a wavepacket, is restored
by a postulate of quantum mechanics
