A hydrogen-like atom (or hydrogenic atom) is any atom or ion with a single valence electron. These atoms are isoelectronic with hydrogen . Examples of hydrogen-like atoms include, but …

operator commutes with both L2 and L z. The total energy operator, the Hamiltonian, may be a reasonable candidate. What is the Hamiltonian here? It is the group of terms within the square …

The Hamiltonian operator for the internal energy of the hydrogen atom is: kinetic energy of internal motion potential energy, Coulomb’slaw. In many textbooks, you will often see the hydrogen …

In quantum mechanics, the Hamiltonian of a system is an operator corresponding to the total energy of that system, including both kinetic energy and potential energy. Its spectrum, the …

hydrogen atom Hamiltonian. Let us now discuss two different choices of basis states for the hydrogen atom, both of which include the electron spin properly. Recall that, in general, for a …

The Hamiltonian operator for the hydrogen atom serves as a reference point for writing the Hamiltonian operator for atoms with more than one electron. Start with the same general form …

So, the full Hamiltonian for a hydrogen-like atom with electron spin in a magnetic eld: H^ = H^ 0 + BB ~ L^ z + g e BB ~ S^ z = H^ 0 + BB ~ (L^ z + g eS^ z); (15.16) note that g e = 2:002322 ’2. …

position and momentum operators of the proton as x^ p;p^ p, and those of the electron as x^ e;p^ e. These are canonical variables, meaning they satisfy the canonical commutation relations: …

13.2 A Hydrogen-like atom A hydrogen-like atom consists of two particles, a nuclei and an electron, bond by a simple Coulomb potential. Figure 13.1: Nucleus and electron bond by …

Consider an arbitrary potential U(r) that only depends on the distance between two particles from the origin. We can write the Hamiltonian simply. One interesting potential of this type arises for …