In nanotechnology, quantum mechanics is crucial for understanding the behavior of electrons and atoms. The Schrödinger equation is a key mathematical tool in this context: \[ \hat{H} \psi = E \psi \] where \( \hat{H} \) is the Hamiltonian operator, \( \psi \) is the wave function, and \( E \) is the energy eigenvalue. Solving this equation allows us to predict the probability distribution of electrons in nanostructures like quantum dots.
