what are electron and hole wave functions? how they overlap
They simply overlap, two electrons are at the same place.. at the same time.
And actually electron orbitals are composed of two electrons, two behave as one particle... you can imagine if two wave functions overlap it's sort of like these two functions become one a.k.a the particles merge. But that depends on your interpretation
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles.
Towards the end of the first lecture for the Qiskit Global Summer School 2025, Foundations of Quantum Mechanics, Olivia Lanes (Global Lead, Content and Education IBM) stated...
Source: https://www.physicsforums.com/insights/quantum-entanglement-is-a-kinematic-fact-not-a-dynamical-effect/
by @RUTA
If we release an electron around a positively charged sphere, the initial state of electron is a linear combination of Hydrogen-like states. According to quantum mechanics, evolution of time would not change this initial state because the potential is time independent. However, classically we expect the electron to collide with the sphere. So, it seems that the quantum and classics predict different behaviours!
The wavefunction of an atomic orbital like ##p_x##-orbital is generally in the form ##f(\theta)e^{i\phi}## so the probability of the presence of particle is identical at all the directional angles ##\phi##. However, it is dumbbell-shape along the x direction which shows ##\phi##-dependence!