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Lecture3 Atoms Electrons and Bonding

# These include the atomic spectrum of hydrogen the

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Unformatted text preview: ar and Walsh point out that there are NO physical assumptions available to “derive” the Schrödenger Equation Schrödinger Equation •Just like Newton’s law of motion, F=ma, and Maxwell’s equations, the Schrödenger Equation was proposed to explain several observations in physics that were previously unexplained. These include the atomic spectrum of hydrogen, the energy levels of the Planck oscillator, non-radiation of electronic currents in atoms, and the shift in energy levels in a strong electric field. Describe accurately the interactions of particles with potential ﬁelds, such as electrons within atoms. (E. Schrödinger, 1926) KE PE 2 Kinetic energy “operator” 2m 2 V ETotal i Potential electron moves through t Energy “operator” Other operators exist: ψ(r,t): “wave function” of electron is a probability amplitude describing the quantum state of a particle. |ψ(r,t)|2 corresponds to the probability density of ﬁnding a Georgia Tech ECE 3080 - Dr. Alan Doolittle particle at a given time, if the particles’ position is measured. V(r) is potential energy by electrostatic ﬁeld. Neudeck and Pierret Table 2.1 EE 332 Spring 2013 Schrödinger Equation in 1D 1D case: ψ(x,t) Separation of variables: ψ (x, t) = ϕ(t) ψ(x) 2 2 ∂ − ∇ Ψ( x ,t ) + V(x)Ψ( x ,t ) = i Ψ( x ,t ) 2m ∂t 2 ∂2 Ψ ( x ) ∂ − Φ( t ) + V(x)Φ( t )Ψ( x ) = i Ψ( x ) Φ( t ) 2 2m ∂ x ∂t Separate variable to obtain the time-dependent and timeindependent...
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