Quantum physics (quantum theory, quantum mechanics)

Uncertainty principle
• Uncertainty principle: (Werner Heisenberg, 1925)
o it is impossible to simultaneously know a particle's exact
position and momentum
p x ħ/2
h = 6.63 x 10 -34 J s = 4.14 x 10 -15 eV·s
ħ = h/(2) = 1.055 x 10 -34 J s = 6.582 x 10 -16 eV·s
(p means “uncertainty” in our knowledge of
the momentum p)
o also corresponding relation for energy and time:
E t ħ/2 (but meaning here is different)
• note that there are many such uncertainty relations
in quantum mechanics, for any pair of
“incompatible”
(non-commuting) observables (represented by
“operators”)
• in general, P Q ½[P,Q]
o [P,Q] = “commutator” of P and Q, = PQ – QP
o A denotes “expectation value”
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