Hamiltonian

(noun)

In quantum mechanics, the observable, denoted by H, that corresponds to the total energy of the system.

Related Terms

Examples of Hamiltonian in the following topics:

  • Quantum Numbers

    • Formally, the dynamics of any quantum system are described by a quantum Hamiltonian (H) applied to the wave equation.
    • There is one quantum number of the system corresponding to the energy—the eigenvalue of the Hamiltonian.
    • There is also one quantum number for each operator (O) that commutes with the Hamiltonian (i.e. satisfies the relation HO = OH).
    • For particles in a time-independent potential, per the Schrödinger equation, it also labels the nth eigenvalue of Hamiltonian (H) (i.e. the energy E with the contribution due to angular momentum, the term involving J2, left out).

  • Description of the Hydrogen Atom

    • The eigenstates of the Hamiltonian (that is, the energy eigenstates) can be chosen as simultaneous eigenstates of the angular momentum operator.

  • Wave Equation for the Hydrogen Atom

    • The eigenstates of the Hamiltonian (that is, the energy eigenstates) can be chosen as simultaneous eigenstates of the angular momentum operator.