Question

Quantum dots (QDs) are a new class of molecule that exhibit totally unique optical properties compared to traditional fluorophores. They are spherical inorganic crystals and their basic properties can be understood as a three-dimensional extension of the particle in a box (PIB) problem. Assuming an infinite potential outside the QD, the normalized wavefunction of a QD electron in its first excited state is \( \psi(r, \theta, \phi) = \left(\frac{1}{2\pi a}\right)^{1/2} \frac{\sin(\frac{\pi r}{a})}{r} \) In reality, the potential at the QD surface is not infinite, but rather some finite value. Explain what impact the finite potential would have on the radial wavefunctions compared to a 3D PIB model.

          Quantum dots (QDs) are a new class of molecule that exhibit totally unique optical properties compared to traditional fluorophores. They are spherical inorganic crystals and their basic properties can be understood as a three-dimensional extension of the particle in a box (PIB) problem. Assuming an infinite potential outside the QD, the normalized wavefunction of a QD electron in its first excited state is \( \psi(r, \theta, \phi) = \left(\frac{1}{2\pi a}\right)^{1/2} \frac{\sin(\frac{\pi r}{a})}{r} \) In reality, the potential at the QD surface is not infinite, but rather some finite value. Explain what impact the finite potential would have on the radial wavefunctions compared to a 3D PIB model.

Quantum dots (QDs) are a new class of molecule that exhibit totally unique optical properties compared to traditional fluorophores. They are spherical inorganic crystals and their basic properties can be understood as a three-dimensional extension of the particle in a box (PIB) problem. Assuming an infinite potential outside the QD, the normalized wavefunction of a QD electron in its first excited state is ψ(r, θ, ϕ) = ((1)/(2π a))^1/2(sin((π r)/(a)))/(r) In reality, the potential at the QD surface is not infinite, but rather some finite value. Explain what impact the finite potential would have on the radial wavefunctions compared to a 3D PIB model.

Added by Claudia R.

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