Matter Waves & Electron Traps: Angular Momentum Explained

[emperrotta]

I am currently reading about matter waves and electron traps.

the textbook states, by the equation:

hf = $$\Delta$$E = E_high - E_low

If an electron confined to a one-dimensional infinite potential well is to absorb a photon, the energy hf of the photon must equal the energy difference $$\Delta$$E between the initial energy level of the electron and a higher level.

Then as an aside, the textbook states:
Although the above equation and what we have discussed about photon absorption and emission can be applied to physical (real) electron traps, they actually cannot be applied to one-dimensional (unreal) electron traps. The reason involves the need to conserve angular momentum in a photon absorption or emission process.

I do not understand this statement about angular momentum.

 

[borgwal]

It's because a photon carries angular momentum, but in 1-D the concept of angular momentum is not defined.

 

[Entropia]

Can you explain it to me?

Sure, I would be happy to explain. The concept of angular momentum is a fundamental principle in physics that describes the rotational motion of objects. In the case of electrons, they also possess angular momentum due to their spinning motion. This angular momentum is conserved in all interactions, including the absorption and emission of photons.

In the context of matter waves and electron traps, the equation hf = ΔE = Ehigh - Elow is based on the assumption that the electron is in a one-dimensional infinite potential well. In this scenario, the electron's angular momentum is not affected by the potential well and remains constant.

However, in a physical electron trap, the potential well is not infinite and can have different shapes and sizes. In this case, the electron's angular momentum can change as it interacts with the potential well. This change in angular momentum must be accounted for in the absorption and emission of photons, as angular momentum must be conserved in all interactions.

In simpler terms, the statement in the textbook is saying that the equation used to describe photon absorption and emission in an ideal one-dimensional infinite potential well cannot be directly applied to physical electron traps because the electron's angular momentum must be considered in these more complex systems.

I hope this helps clarify the concept of angular momentum in the context of matter waves and electron traps. Let me know if you have any further questions.