University Physics II

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University Physics II

• Schrödinger waves, a.k.a. wave mechanics

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Inspiration
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Reference

• Chalmers Sherwin, Introduction to Quantum
  Mechanics, Holt, Rinehart and Winston, 1959

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Postulates for a two-particle systemPostulate 1

• The wave function ?, belonging to a system
  composed of two particles, is a function of their
  positions in configuration space (x1,y1,z1) and
  x2,y2,z2)

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Postulate II

• The wave equation for ? is obtained from the
  classical expression for the total energy of the
  system by replacing the dynamical variables by
  operators

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Postulate III

• The wave function ? and all its spatial
  derivatives must be everywhere continuous,
  finite, and single valued, throughout the full
  range of the six configuration variables

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Postulate IV

• We say that ? is normalized, that is that
• ???dx1dy1dz1dx2dy2dz2 1
• Where the integration is over all the
  six-dimensional configuration space

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Postulate V

• The expectation value of an observable A, is
  calculated from
• Aav ??A(x,p)? dx1dy1dz1dx2dy2dz2

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The Schrödinger Equation

• Classical conservation of energy equation
• KE PE E in one dimension
• P2/(2m) V(x) E
• Substitute the operators for P and x and E and
  let them act on ?
• -h2/(8p2m)?2?/?x2 V(x) ? _(h/(2pi))??/?t