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Presentation transcript:

Quantum Chemistry Revisited Powerpoint Templates

Wave Equation Non Relativistic Limit Possible solution: Plane waves

Time Independent Schrödinger Equation

Time dependent Schrödinger Equation

Lousy relativistic equation 2nd derivative in space 1st derivative in time Many fathers equation (Klein, Fock, Schrödinger, de Broglie, ...) Klein-Gordon Equation (1926)

(E – V)2 = p2c2 + m2c4 Free Electron (V = 0)

Klein-Gordon Equations Eigen values for E2 ± E solutions Matter Antimatter Carl Anderson discovers the positron in 1932 KG works well for bosons (integer spin particles)

a = b = 1 ab + ba = 0

3 dimensions and time

Dirac Equation 2 positive solutions 2 negative solutions Matter / Antimatter Spin ± ½

Pauli Matrices

There cant be flow in pure real and pure imaginary wave functions. In stationary states the flow is either zero or constant. div D = ρ implies that stationary states create static electric fields. rot H = J + D/t implies that stationary states with J≠0 create static magnetic fields. Static magnetic fields induce currents J which create induced magnetic fields. Time dependent magnetic fields induce time dependent electric fields (rot E = - B/t), which means time dependent charge densities to which correspond non stationary states.