Transcription of 1 Complex Numbers in Quantum Mechanics
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1 Complex Numbers in Quantum Mechanics
1 Complex Numbers in Quantum MechanicsComplex Numbers and variables can be useful in classical physics. However, theyare not essential. To emphasize this, recall that forces, positions, momenta, potentials,electric and magnetic fields are all real quantities, and the equations describing them,Newton s laws, Maxwell s equations,etc. are all differential equations involving strictlyreal Mechanics is different. Factors ofi= 1 are everywhere, for examplefrom Heisenberg we have his famous commutation relation,QP P Q=i h,and from Schr odinger his equally famous equation hi t =H.
component along the y axis, and one along the x axis. Only the component along the y axis gets transmitted, and the transmitted intensity satisfies the classical Malus Law: I(θ) = I(0)cos2 θ, (4) where I(θ) is the intensity of transmitted light, when the incident light is polarized at angle θ to the axis of the polarizer. This is all well-known seemingly pure classical physics.
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