# Quantum Dots and the "Particle in a 1-D Box" Model

1. Nov 4, 2014

### spaghettibretty

1. The problem statement, all variables and given/known data

The "particle in a box" is the simplest quantum system. Despite this, it still reveals a lot of important new quantum features. Please use the "particle in a 1-D box" model to explain the reason why when the size of a quantum dot gets smaller, the wavelength of the emitted photon due to the n=1⇒n=2 transition becomes shorter (color shifts to blue).

2. Relevant equations

speed of light = wavelength * frequency
(it isn't listed in the question, but I use it for my answer)

3. The attempt at a solution

I'm not really sure how to tackle this question and give a sufficient answer. I tried reading around on the "particle in a 1-D box" model as well as quantum dots, but I'm not sure what I'm saying is sufficient.

My current answer is basically that the oscillation period of a particle in a 1-D box will decrease if the length of the box is reduced. A lower oscillation period equals a higher frequency, which, in turn, equals a lower wavelength. Therefore, if the length of the box decreases, the oscillation period decreases, and the wavelength decreases. This can be applied to a quantum dot. As the quantum dot's size is reduced, the frequency of its emitted photons will rise and cause the wavelength of those photons to decrease. The decreasing of the wavelength means that the perceived color of the photons will be more blue in comparison.

Is this answer enough? Are its components even correct? This material wasn't really covered by my professor and it's more of a self-research problem.

2. Nov 4, 2014

### BvU

Oscillation period of a particle in a 1-D box ? It's abox, not a (harmonic) oscillator . The question is about photons that are emitted when transitions from higher energy levels to lower energy levels occur. (n=1 ⇒ n=2 is not one of these; an error in the text ?).

3. Nov 4, 2014

### spaghettibretty

Oh, my mistake. It's suppose to be n=2⇒n=1. If the oscillation period thing is incorrect, that pretty much tears down my whole argument.
On another thought, I also know that if there are more nodes in the 1-D box, then there is a higher energy and higher energy equals higher frequency. However, I'm not sure how that ties in with the quantum dots.

4. Nov 5, 2014

### BvU

It's not about the particles themselves. It's about the energy change of the (charge carrying) particles when they go from a higher energy state to a lower energy state. That energy difference is sent off in the form of a photon. So you want to find an expression for the energies of the possible states, and see if these depend on the size of the box. (A quantum dot is considered as a box here).

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