From Harmonic Oscillators to Quantum Gravity

Canonical quantization (CQ) has been successful in solving many problems, and is a tool used for nearly all cases. But CQ has not worked well for some problems that have resisted any acceptable solution. Happily, the harmonic oscillator, with -? < p,q < ?, is well solved. However, for the half-harmonic oscillator, where -? < p < ? while 0 < q < ? CQ fails significantly. Likewise, quantum gravity has failed with CQ as well. A new quantization process called affine quantization (AQ) will be introduced. AQ leads to acceptable solutions for the half-harmonic oscillator and shows considerable success for quantum gravity. This lecture will demonstrate the solution of the half-harmonic oscillator and leads to a meaningful Schrödinger equation for quantum gravity, which is in position to seek appropriate solutions from complex differential equations.

Host: Sergei Shabanov