Lecture12_QM4

Lecture12_QM4 - 1 Quantum Theory Quantum Theory 4 4 2...

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Unformatted text preview: 1 Quantum Theory Quantum Theory 4 4 2 Topics Topics The 1-D Square Well The 1-D Harmonic Oscillator Quantum Tunneling Summary 3 Recap Recap 1887 1961 = H t it ) ( 2 2 2 r V m H + - = = h/2p In late 1925, building on de Broglies idea, Erwin Schrdinger proposed the following wave equation is a complex number called the wavefunction 1887 1961 4 Recap Recap p ( x ) = 2 = (29 (29 p ( x ) dx is the probability to find a particle between x and x + dx x x x + dx p ( x ) Max Born 1882 1970 5 The 1-D Square Well The 1-D Square Well 6 The 1-D Square Well The 1-D Square Well + - = ) ( 2 2 2 2 x V x m t i t t = ) ( x V = ) ( x V ) ( = x V An object of mass m in a 1-D well with impenetrable walls 7 The 1-D Square Well The 1-D Square Well + - = ) ( 2 2 2 2 x V x m t i t t If the potential energy function V ( x ) is independent of time, we can write the solution of the Schrdinger equation in the separable form ( , ) ( ) ( ) x t x t = 8 The 1-D Square Well...
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This note was uploaded on 02/17/2010 for the course PHY PHY3101 taught by Professor Prosper during the Spring '10 term at FSU.

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Lecture12_QM4 - 1 Quantum Theory Quantum Theory 4 4 2...

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