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量子物理学研究

Research plan

Understand the combinatorics by

• Understanding Kim and Zeng's combinatorial interpretation of orthogonal polynomials.
  • Understand how the trees specialize in various cases.
  • Understand if this series A108457 offers a different interpretation for the trees.
  • Find or create a software program to enumerate and count the relevant trees. Or learn how to use Sage and Sage-Combinat
  • Understand how orthogonality works.
  • Understand what it means for the hydrogen atom.
  • Understand what it means for the radial equation.
  • Understand spherical harmonics.
• Understand the Wick contraction, Wick's theorem and Isserlis's theorem.
• Ask for help regarding the various combinatorial interpretations.

Understand the measurement of observables

• Write up the combinatorics of the orthogonality of the Hermite polynomials.
• Investigate how to interpret the calculation of observables.

Extend my combinatorial research into orthogonal polynomials by considering spacetime, the creation and annihilation of particles, spin and spinors.

• Understand in Griffiths the relation between angular momentum and spin.
• Understand the Dirac equation and any cases of exact solutions.
• Understand the hydrogen atom in the nonrelativistic and relativistic cases.
• Understand the combinatorics of the free particle.
• Understand Feynman diagrams.

Other steps to take from earlier

• Fix up the description of the hydrogen atom.
• Study how the probabilist Hermite polynomials fit with the normal distribution, and how they are orthogonal.
• Relate the physicist Hermite polynomials to the probabilist Hermite polynomials.
• Provide a picture of the Legendre polynomials.
• Find a combinatorial interpretation of the associated Legendre functions.
• Suggest how the energy levels, assembled from individual empty cells, relate to choice frameworks, and whether or not there is anything to observe. It takes energy to support an observation of nothing.

Ideas

The configurations into one-cells and two-cells are into nonentanglements and entanglements. And entanglements exist as a possiblity from the beginning, not just as something that can happen.