Thanks! Yes, it has begun to dawn on me that since d/dt e^(iwt) = iwe^(iwt) (frequency w, time t) that e^(iwt) is both an eigenvector of simple versions of

Thanks! Yes, it has begun to dawn on me that since d/dt e^(iwt) = iwe^(iwt) (frequency w, time t) that e^(iwt) is both an eigenvector of simple versions of Schrödinger's equation and also, essentially via Fourier theory, one axis of an orthogonal basis of a linear algebra (or Hilbert space if prefer that since it permits infinitely many orthogonal basis vectors) representation of quite general wave function solutions to the equation. And just by including more basis vectors, can get whatever level of accuracy we might want. That is, the terns in the Fourier transform act like the coefficients in the linear combination of basis vectors, the linear combination that approximates the wave function solution of Schrödinger's equation. So, essentially we are into harmonic motion, e.g., swinging pendulums, whether we wanted to be or not. Then we are ready to guess that for treatment of the electron in a hydrogen atom we will be into something like Sturm-Liouville theory of two point boundary value problems and standing waves, vibrating violin strings, etc. That is, an electron in what it does with a hydrogen nucleus will be like a vibrating violin string. Thanks.