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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, nonradiation 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 timedependent and timeindependent...
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This document was uploaded on 02/18/2014.
 Spring '09

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