Quantum Chemistry Revisited Powerpoint Templates Page 1 Wave

Quantum Chemistry Revisited Powerpoint Templates Page 1

Wave Equation Non Relativistic Limit Possible solution: Plane waves Powerpoint Templates Page 2

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Time Independent Schrödinger Equation Powerpoint Templates Page 4

Time dependent Schrödinger Equation Powerpoint Templates Page 5

Lousy relativistic equation 2 nd derivative in space 1 st derivative in time Many fathers equation (Klein, Fock, Schrödinger, de Broglie, . . . ) Klein-Gordon Equation (1926) Powerpoint Templates Page 6

(E – V)2 = p 2 c 2 + m 2 c 4 Free Electron (V = 0) Powerpoint Templates Page 7

Klein-Gordon Equations Eigen values for E 2 ± E solutions Matter Antimatter Carl Anderson discovers the positron in 1932 KG works well for bosons (integer spin particles) Powerpoint Templates Page 8

a=b=1 ab + ba = 0 Powerpoint Templates Page 9

3 dimensions and time Powerpoint Templates Page 10

Dirac Equation 2 positive solutions 2 negative solutions Matter / Antimatter Spin ± ½ Powerpoint Templates Page 11

Pauli Matrices Powerpoint Templates Page 12

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ØThere cant be flow in pure real and pure imaginary wave functions. ØIn stationary states the flow is either zero or constant. Ødiv D = ρ implies that stationary states create static electric fields. Ørot H = J + D/ t implies that stationary states with J≠ 0 create static magnetic fields. ØStatic magnetic fields induce currents J which create induced magnetic fields. ØTime dependent magnetic fields induce time dependent electric fields (rot E = - B/ t), which means time dependent charge densities to which correspond non stationary states. Powerpoint Templates Page 16