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05_02_14 - 35 3 The wave-particle duality and bound states...

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[email protected] 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). ϖ ! ! = = E k p , ] [ ) ( 0 2 0 2 2 ) ( 1 2 V k V E m k m p + = + = ϖ 02/14/2005
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[email protected] 36 A wave equation for an oscillating string Λ Λ = = = Λ = = 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 RVFLOODWLRQV±RI±WKH±IRUP ]) [ sin( ) , ( t v x k A t x y - =
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