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The radial Green’s functions for the N‐dimensional free‐particle, isotropic harmonic oscillator and Coulomb problems all contain a product of two Bessel or Whittaker functions. After integral representations for these respective products are introduced, each Green’s function exhibits the structure of a Fourier transform. One obtains thereby the Feynman propagators K(r1,r2,t) for the free particle and harmonic oscillator. In the Coulomb case, the Fourier transform involves the quantum number variable and leads instead to the recently defined Sturmian propagator. The well‐known connection between Coulomb and oscillator eigenstates of various dimensionality is manifested in a new way by the structure of the propagators derived here

Propagators from integral representations of Green’s functions for the N-dimensional free-particle, harmonic oscillator and Coulomb problems