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The ladder operators of the quantum harmonic oscillator or the "number representation" of second quantization are just special cases of this fact. Ladder operators then become ubiquitous in quantum mechanics from the angular momentum operator, to coherent states and to discrete magnetic translation operators.
In quantum mechanics, the angular momentum operator is one of several related operators analogous to classical angular momentum. The angular momentum operator plays a central role in the theory of atomic and molecular physics and other quantum problems involving rotational symmetry. Being an observable, its eigenfunctions represent the ...
The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary smooth potential can usually be approximated as a harmonic potential at the vicinity of a stable equilibrium point, it is one of the most important model systems in quantum mechanics.
In physics, the Clebsch–Gordan (CG) coefficients are numbers that arise in angular momentum coupling in quantum mechanics. They appear as the expansion coefficients of total angular momentum eigenstates in an uncoupled tensor product basis. In more mathematical terms, the CG coefficients are used in representation theory, particularly of ...
Orbital angular momentum operators have the ladder operators: = which raise or lower the orbital magnetic quantum number m ℓ by one unit. This has almost exactly the same form as the spherical basis, aside from constant multiplicative factors.
Creation and annihilation operators. Creation operators and annihilation operators are mathematical operators that have widespread applications in quantum mechanics, notably in the study of quantum harmonic oscillators and many-particle systems. [1] An annihilation operator (usually denoted ) lowers the number of particles in a given state by one.
Spin (physics) Spin is an intrinsic form of angular momentum carried by elementary particles, and thus by composite particles such as hadrons, atomic nuclei, and atoms. [1][2]: 183 –184 Spin is quantized, and accurate models for the interaction with spin require relativistic quantum mechanics or quantum field theory.
Angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity – the total angular momentum of a closed system remains constant. Angular momentum has both a direction and a magnitude, and both are conserved.