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Unformatted text preview: Georg.Hoffstaetter@Cornell.edu 35 3) The wave-particle duality and bound states The wave character of light and the photon character of light are both but different manifestations of the same thing. Similarly the particle character of electrons, atoms, and neutrons and their wave character are both but different manifestations of the same thing. Free particles: Particles in a potential: (non-relativistic) To describe waves more generally, one needs a wave equation for this dispersion relation Z (k). ! ! = = E k p , ! " # $ % ] [ ) ( 2 2 2 ) ( 1 2 V k V E m k m p + = + = & & 02/14/2005 Georg.Hoffstaetter@Cornell.edu 36 A wave equation for an oscillating string = = = = = T t v x t x T t x v t x y t x y y y x m y m y x T 2 1 ; ) , ( ) , ( 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 02/14/2005 x y x T y T F x y 2 2 = = x $ VWULQJ ZLWK XQLIRUP PDVV SHU OHQJWK VXSSRUWV...
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