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# lec 3 - The Schrdinger Equation Reading OGC(4.6 and(5.1 The...

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The Schrödinger Equation Reading: OGC: (4.6) and (5.1)

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III - 2 The Person Behind The Science Erwin Schrödinger 1887-1961 In 1927 Schrödinger moved to University of Berlin as Planck's successor Develops his wave equation in 1926 Moments in a Life Highlights Born and educated in Vienna Received Nobel Prize in Physics with Paul Dirac (1933)
III - 3 The Schrödinger Equation H Ψ = E Ψ y H is the Hamiltonian Operator; you can’t “cancel” the Ψ — “Cancelling” the Ψ is like “cancelling” the x in f(x) = mx. You just can’t do it. y Our goal is to operate on Ψ (using the H Operator) and get an energy (E) multiplied by the same Ψ .

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III - 4 Deriving the Schrödinger Equation Total Energy = Kinetic Energy + Potential Energy E = KE + PE y This equation describes the energy of an electron: y Start with this classical equation. y Use classical and quantum mechanical relationships to find the Hamiltonian Operator (H). y Find values of Ψ that fit the Schrödinger Equation: H Ψ = E Ψ .
III - 5 f x f y — If f(x,y,z) = x 2 +y 3 +z 4 , Describing Kinetic Energy (KE) Classically: Quantum Mechanically: then = 2x and = 3y 2 p x = ih 2 π ∂Ψ x KE = 1 2 mv 2 p = mv, so KE = p 2 2m Combining Equations: (close enough for now!) = h 2 8m π 2 2 Ψ ( ) (

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