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Bloch Sphere Template

Bloch Sphere Template
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2019-12-11 19:47
VectorTrigonometrySolid GeometryComplex NumberGeometric Construction
This example demonstrates the geometric construction and visualization of a Bloch Sphere. It involves core mathematical concepts such as sphere, vector, rotation, parametric equations, and complex number representation. GeoGebra commands like Intersect, Sphere, Line, Rotate, Vector, and Distance are used, along with objects like phi, theta, B, A, a, C, f, alpha, XZ, u, X, Y, Z, B1, v, w, k, b, u1. Suitable for high school and above students in mathematics, physics, or engineering to understand the Bloch Sphere model in quantum mechanics or complex analysis.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, zAxis) → A
  2. Sphere(A, B) → a
  3. Line(A, C) → f
  4. Rotate(B, (π * alpha / 8), f) → XZ
  5. Vector(A, XZ) → u
  6. Rotate(B, (alpha / 8 * π), xAxis) → X
  7. Rotate(B, (alpha / 8 * π), yAxis) → Y
  8. Rotate(B, (π * alpha / 8), zAxis) → Z
  9. Vector(A, X) → v
  10. Vector(A, Y) → w
  11. Vector(A) → k
  12. Distance(A, B) → b
  13. Vector(A, B) → u1