Physics Seminar

We derive the mu-wavelets (“nature’s wavelets”) as constrained minimum Heisenberg uncertainty states and investigate their relationship to the harmonic oscillator. We show that the dual vectors that are bi-orthogonal to the mu-wavelets are the Hermite polynomials. The mu-wavelets are a complete basis on the Schwartz space (a sub-space of Hilbert space). Given time, we discuss the natural SUSY structure of the resulting “minimum uncertainty harmonic oscillator” and derive generalized “super-coherent states” using the displacement operator approach analogous to that of Perelomov.