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...

physics, Hamiltonian mechanics is a reformulation of Lagrangian mechanics that emerged in 1833. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics...

systems, the goal of quantum mechanics in non-perturbative regimes is to find the eigenvalues and eigenvectors of a Hamiltonian of the form H = H s +...

system Hamiltonian (quantum mechanics), an operator corresponding to the total energy of that system Dyall Hamiltonian, a modified Hamiltonian with two-electron...

observable commutes with the Hamiltonian, the quantum number is said to be "good", and acts as a constant of motion in the quantum dynamics. To fully specify...

Quantum superposition is a fundamental principle of quantum mechanics that states that linear combinations of solutions to the Schrödinger equation are...

mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics. This mathematical formalism...

constant of motion. In other words, the quantum number is good if the corresponding observable commutes with the Hamiltonian. If the system starts from the eigenstate...

These systems can be studied in both Hamiltonian mechanics and dynamical systems theory. Informally, a Hamiltonian system is a mathematical formalism developed...

in quantum mechanics. Furthermore, it is one of the few quantum-mechanical systems for which an exact, analytical solution is known. The Hamiltonian of...

Quantum thermodynamics is the study of the relations between two independent physical theories: thermodynamics and quantum mechanics. The two independent...

Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. It was the first conceptually...

quantum entanglement is at the heart of the disparity between classical and quantum physics: entanglement is a primary feature of quantum mechanics not...

the phase-space formulation is that it makes quantum mechanics appear as similar to Hamiltonian mechanics as possible by avoiding the operator formalism...

By contrast, in non-relativistic quantum mechanics, terms have to be introduced artificially into the Hamiltonian operator to achieve agreement with...

leading to the development of analytical mechanics (which includes Lagrangian mechanics and Hamiltonian mechanics). These advances, made predominantly in...

which can be explained by classical mechanics. Beginning out of attempts to extend the understanding of quantum mechanics, the theory has developed in several...

duality Wightman axioms WKB approximation quantum mechanics, matrix mechanics, Hamiltonian (quantum mechanics) particle in a box particle in a ring particle...

summarizes equations in the theory of quantum mechanics. A fundamental physical constant occurring in quantum mechanics is the Planck constant, h. A common...

atomic, molecular, and optical physics and quantum chemistry, the molecular Hamiltonian is the Hamiltonian operator representing the energy of the electrons...

mathematics, Nambu mechanics is a generalization of Hamiltonian mechanics involving multiple Hamiltonians. Recall that Hamiltonian mechanics is based upon...

of quantum mechanics, and is used for calculating geodesic motion in general relativity. Canonical transformations The invariance of the Hamiltonian (under...

this constraint has yet to be found. A plausible candidate for the quantum Hamiltonian constraint is the operator introduced by Thiemann. The constraints...

physics, mechanics is the study of objects, their interaction, and motion; classical mechanics is mechanics limited to non-relativistic and non-quantum approximations...

mid-century. Quantum tunnelling falls under the domain of quantum mechanics: the study of what happens at the quantum scale, which classical mechanics cannot...

In quantum mechanics, an energy level is degenerate if it corresponds to two or more different measurable states of a quantum system. Conversely, two or...

In physics, non-Hermitian quantum mechanics, describes quantum mechanical systems where Hamiltonians are not Hermitian. Parity–time (PT) symmetry was initially...

Quantum statistical mechanics is statistical mechanics applied to quantum mechanical systems. In quantum mechanics a statistical ensemble (probability...

The old quantum theory is a collection of results from the years 1900–1925 which predate modern quantum mechanics. The theory was never complete or self-consistent...

a glossary for the terminology often encountered in undergraduate quantum mechanics courses. Cautions: Different authors may have different definitions...