Angular Momentum
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Angular Momentum: A measure of the amount of rotation a particle has, taking into account its mass, shape, and speed. In quantum mechanics, it is quantized and has discrete values. Eigenfunction: A function that is associated with a particular operator in quantum mechanics, where the operator acting on the function yields the function multiplied by a constant (the eigenvalue). Eigenvalue: The constant value obtained when an operator acts on its eigenfunction. It represents measurable quantities in quantum mechanics. Commutator: An operation used to determine whether two operators can be simultaneously measured. It is defined as [A, B] = AB - BA. Simultaneous Eigenfunctions: Functions that are eigenfunctions of two or more operators at the same time, indicating that the corresponding physical quantities can be simultaneously measured. Uncertainty Principle: A fundamental concept in quantum mechanics stating that certain pairs of physical properties, like position and momentum, cannot be simultaneously measured with arbitrary precision. Standard Deviation: A measure of the spread or dispersion of a set of values. In quantum mechanics, it represents the uncertainty in a measured property. Orbital Angular Momentum: The component of angular momentum associated with the motion of a particle through space, distinct from spin angular momentum. Spin Angular Momentum: An intrinsic form of angular momentum carried by particles, independent of their motion through space. Spherical Coordinates: A coordinate system used to describe the position of a point in space using three values: the radial distance, the polar angle, and the azimuthal angle. Ladder Operators: Operators used to raise or lower the eigenvalue of another operator, often used in the context of angular momentum. Normalization: The process of adjusting the magnitude of a function so that its total probability density equals one. Degeneracy: The condition where two or more eigenfunctions correspond to the same eigenvalue, indicating multiple states with the same energy. Associated Legendre Functions: Special functions used in the solution of angular momentum problems in quantum mechanics. Spherical Harmonics: Functions that describe the angular part of the wavefunction in spherical coordinates, often used in the context of angular momentum.