Chapter 11: Generalized Periodic Functions

The following sections are included:

• Scope of this Chapter

• Particle-in-a-Box

• Square Periodic Functions

  • Hamiltonian Formulation

  • SPF as Generalized Trigonometric Functions

• Analytical Periodic Solutions to f(t)² + g(t)² =1

  • Generalized Cosine and Sine Functions

  • Calculation of Phase Function – θ(t)

  • Differential Equations for f(t) and g(t)

  • An Explicit Example

  • Jacobi Elliptic Functions

  • Comments

• Leah-Cosine and -Sine Functions

  • Three Leah Periodic Functions

  • Determination of r(θ)

  • Comments

• Comments and References

• Bibliography