Discussion
\(-\frac{\hbar^{2}}{2}\left(\frac{1}{me} + \frac{1}{mh}\right)\) \(\frac{d^{2}\psi}{dx^{2}}\) \(+ \frac{z^{2}}{4\pi r}\cdot\Psi = E\Psi\) could be a Schrödinger equation for :
Answer: D
It could be the equation for two charged particles in 1-D box problem.
Read the equation term by term. The kinetic energy term carries (1/me + 1/mh), which is 1/μ, the reciprocal of the reduced mass of two particles, so two particles are moving relative to each other. It has only d2/dx2, so the motion is in one dimension. The potential term varies as z2/r, a Coulomb interaction between charges. Together these describe two charged particles, such as an electron and a hole, confined in one dimension.
A single particle in a box has one mass and no potential inside the box. A 2D box would need derivatives in two coordinates. Simple harmonic motion would need a potential proportional to x2, not to 1/r.
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