Exponential Hamiltonian: Convergence in an iterated product representation for a linear harmonic oscillator

Abstract

Using an iterated product representation of an exponential Hamiltonian, the density matrix for the potential V(x) = 1/2 K x 2 is derived in nth‐order approximation. The density matrix so found is shown to converge to the exact quantum mechanical result in the limit of n → ∞ .