Quantum Mechanics Of One- And Two-electron Atoms Pdf Site

The Hamiltonian for a two-electron atom is:

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.

H = -ℏ²/2m ∇² - Ze²/r

The Hamiltonian for a one-electron atom is:

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: quantum mechanics of one- and two-electron atoms pdf

where r₁ and r₂ are the distances between the electrons and the nucleus, and r₁₂ is the distance between the two electrons.

H = -ℏ²/2m (∇₁² + ∇₂²) - Ze²/r₁ - Ze²/r₂ + e²/r₁₂ The Hamiltonian for a two-electron atom is: where

A classic topic in physics!

The two-electron atom, also known as the helium-like atom, consists of two electrons orbiting a nucleus with atomic number Z. The time-independent Schrödinger equation for this system is: H = -ℏ²/2m (∇₁² + ∇₂²) - Ze²/r₁

Hψ = Eψ