Discussion Overview
The discussion revolves around deducing the units of angular frequency (\(\omega\)) and the reduced Planck's constant (\(\hbar\)) in the context of a calculation presented in Paul Harrison's book on quantum wells. Participants are trying to reconcile the numerical values provided with their respective units to ensure consistency with the energy value of 871.879 meV.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
- Mathematical reasoning
Main Points Raised
- One participant notes that \(\hbar\) is given as \(6.58214928 \times 10^{-13} \text{ meV}\) and infers \(\omega\) to be \(9.9879927\), questioning the units of \(\omega\) and \(\hbar\).
- Another participant clarifies that in certain units, \(\hbar\) is \(6.5821 \times 10^{-13} \text{ meV s}\), suggesting that \(\omega\) could be \(1.325 \times 10^{15} \text{ radians/seconds}\).
- Some participants express confusion about the units of \(\hbar\) and \(\omega\), with one stating that arbitrary units could be used for \(\hbar\) but questioning the validity of the numerical value of \(87.2827...\).
- There is a claim that the initial calculation of \(\omega\) was incorrect, with a participant asserting that it should be \(1.32 \times 10^{15} \text{ radians/seconds}\) and challenging the use of units for \(m_0\).
- Another participant points out that \(\hbar\) has units of meV s and that \(\omega\) has units of \(s^{-1}\), which would yield the correct units for the product \(\hbar \omega\) as meV.
Areas of Agreement / Disagreement
Participants express differing views on the units of \(\hbar\) and \(\omega\), with no consensus reached on the correct interpretation of the values and units involved in the calculations.
Contextual Notes
There are unresolved questions regarding the assumptions made in the calculations, particularly concerning the units used for mass and the numerical values of constants. The discussion highlights the complexity of unit conversions and the importance of clarity in definitions.