OAI/MathematicalPhysics/ContinuumCoulomb/OneParticle/VerticalMode.lean

GitHub source file

14 declarations, 0 contain sorry, 0 declared as axioms

The actual normalized Gaussian in the transverse direction.

  1. def OAI.ContinuumCoulomb.verticalMode line 15
  2. theorem OAI.ContinuumCoulomb.verticalMode_positive line 18
  3. theorem OAI.ContinuumCoulomb.verticalMode_smooth line 22
  4. theorem OAI.ContinuumCoulomb.verticalMode_hasDerivAt line 26
  5. theorem OAI.ContinuumCoulomb.verticalMode_deriv line 35
  6. theorem OAI.ContinuumCoulomb.verticalMode_second_hasDerivAt line 39
  7. theorem OAI.ContinuumCoulomb.verticalMode_second_deriv line 49
  8. theorem OAI.ContinuumCoulomb.verticalMode_square line 53
  9. theorem OAI.ContinuumCoulomb.verticalMode_moment_integrable line 60
  10. theorem OAI.ContinuumCoulomb.verticalMode_square_integrable line 69
  11. theorem OAI.ContinuumCoulomb.verticalMode_normalized line 73
  12. theorem OAI.ContinuumCoulomb.verticalMode_memLp line 79
  13. theorem OAI.ContinuumCoulomb.verticalMode_deriv_square_integrable line 83
  14. theorem OAI.ContinuumCoulomb.verticalMode_deriv_memLp line 91