Wednesday, 27 May 2020

quantum mechanics - Heisenberg Uncertainty principle defined as DeltaxDeltapxgeqh versus DeltaxDeltapxgeqhbar/2



At my university, in the during lectures and in the equation sheet for our exams, the formula for the Heisenberg Uncertainty Principle is stated as ΔxΔpxh, for example in one of my lecture notes, the following example is illustrated using this formula


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However I know that in my textbook (University Physics by Young and Freedman) and pretty much universally the Heisenberg Uncertainty Principle is stated as ΔxΔpx2. Using this formula, we can see the example above is off by a factor of 4π.


Is the formula, ΔxΔpxh, that my university uses a valid formula? If so is just a weaker version of ΔxΔpx2?




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