where ν is the frequency in cycles per second. In other words, one can add or subtract
E = nhν of energy where n ≥ 0. The second quantum effect stems from the fact that if an oscillator were
able to come completely to rest, ∆x would be zero and this would violate the ∆x∆p ≥ ¯h/2 limitation. The
4result is that there is a minimum energy of E = hν /2, i.e. the oscillator energy can only take on the values
E = (n + 1/2)hν which can never become zero since n cannot be negative. Louis J.

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