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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.

experiment. At this level, quantum probability is like coin-tossing. One cannot say what the outcome will be for a toss of an individual coin. Many tosses are needed to see that the chance of “heads” is 0.50 for an unbiased coin. The idea of “hidden” variables in quantum mechanics can be explained using coin tosses. While we say that ...

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