Hey everyone, So I've been a little bit confused about something, and I'd like some input on this: When I look at systems like the particle in a box, or the Hydrogen Atom, it's clear that the higher energy states of comparable shape have more nodes. This seems to always be true. For any orbital, the number of radial nodes increases with increasing principal quantum number and with nodes of a given principal quantum number, the number of nodes, and the energy increases as the angular momentum quantum number increases. In the particle in a box system, as the characteristic quantum number increases, the number of nodes, and the energy increases. In molecular orbitals of a molecular system, orbitals with more nodes have higher energy than those with fewer nodes (whether in the simple homonuclear H2 or something more complicated systems like Benzene). So it seems like nodes implies energy. If that's the case why? With electrons, I have heard (and can believe) rationalizations based on electrostatic attractions and repulsions. For instance, in the antibonding MO of H2, the antibonding orbital places most of the electron density by the nuclei which raises the electrostatic potential energy of the system. Even for a particle in a box, where the particle is an electron, I can see that because by creating nodes, you're concentrating electron density in smaller volumes. My contention with that explanation though is that it hinges on electrostatic potential energy and that the nodes creating energy thing seems more general. Am I wrong? It seems to me like the creation of nodes to some degree decreases uncertainty because the quantum particle is being more localized. If that happens, then doesn't the zero point energy and the corresponding energies increase?