- #1
Alephu5
- 11
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Given the relationships: [itex]\lambda = \frac{h}{p} = \frac{h}{mv}[/itex] and [itex]E = hf[/itex] for wavelike non-relativistic matter, and [itex]v = \lambda f[/itex] for a general wave, one can obtain the result:
[itex]E = \frac{h^2}{m \lambda^2}[/itex].
Whilst for particulate matter, we have [itex]E = \frac{1}{2}mv^2[/itex], which when combined with the assumptions above gives:
[itex]E = \frac{h^2}{2m \lambda^2}[/itex] which is the generally accepted answer.
Does anyone know why these two results differ by a factor of 2 and why the first is incorrect?
[itex]E = \frac{h^2}{m \lambda^2}[/itex].
Whilst for particulate matter, we have [itex]E = \frac{1}{2}mv^2[/itex], which when combined with the assumptions above gives:
[itex]E = \frac{h^2}{2m \lambda^2}[/itex] which is the generally accepted answer.
Does anyone know why these two results differ by a factor of 2 and why the first is incorrect?