Wave Functions - Assumptions and Redefinitions

While watching a lecture from MIT Open Courseware titled "Operators and the Schrodinger Equation" I was struck when the professor listed as an assumption in his definition of the wave function that it must of needs be continuous.

If we dismiss this malady as ignorant in light of tunneling then all quantum mechanics collapses as well as our estimates on:

  1. Age of the universe
  2. Size of the universe
  3. Speed of light variation near gravity wells

To be sure the direction we are led to by the trend is a much larger, older universe, logically the recurrent one suggested by Penrose recently.

The ideal model for this is gap theory, as in gap junctions of neurology, where a space between neurons causes acceleration of the signal.  A gap leads to a leap: signals want identity resonance in similar.

So while wave-particle duality is not presupposed on the double-slit experiment as we discussed earlier, the idea of jumping between nodes supercedes classic wave identity as being a continuous function.

To induce tunneling perhaps all that is needed are resonant nodes between the gap for the wave to leap.