Quantum Mechanics Of One- And Two-electron Atoms Pdf May 2026

The one-electron atom, also known as the hydrogen-like atom, consists of a single electron orbiting a nucleus with atomic number Z. The time-independent Schrödinger equation for this system is:

The Hamiltonian for a one-electron atom is: quantum mechanics of one- and two-electron atoms pdf

where ℏ is the reduced Planck constant, m is the electron mass, e is the elementary charge, and r is the distance between the electron and the nucleus. The one-electron atom, also known as the hydrogen-like

H = -ℏ²/2m ∇² - Ze²/r

where r₁ and r₂ are the distances between the electrons and the nucleus, and r₁₂ is the distance between the two electrons. The one-electron atom