angular momentum operatorの例文

• The operator, specifically called the " orbital angular momentum operator ".
• That is, the commutator for the angular momentum operators are then commonly written as
• And these are essentially the commutators the orbital and spin angular momentum operators satisfy.
• Examples are the total angular momentum operators.
• Many terms in the Hamiltonians of atomic or molecular systems involve the scalar product of angular momentum operators.
• The commutator of any two angular momentum operators ( corresponding to component directions ) is non-zero.
• In simpler terms, the total angular momentum operator characterizes how a quantum system is changed when it is rotated.
• But this is fundamentally the same thing, because of the close mathematical relation between rotations and angular momentum operators .)
• The angular momentum operator plays a central role in the theory of atomic physics and other quantum problems involving rotational symmetry.
• The term " angular momentum operator " can ( confusingly ) refer to either the total or the orbital angular momentum.
• In quantum mechanics, each Pauli matrix is related to an angular momentum operator that corresponds to an observable describing the isospin operator.
• Creation and annihilation operators can be constructed for spin-objects; these obey the same commutation relations as other angular momentum operators.
• The relationship between the angular momentum operator and the rotation operators is the same as the relationship between lie algebras and lie groups in mathematics.
• (In practice, when working through this math, we usually apply angular momentum operators to the states, rather than rotating the states.
• In quantum mechanics, the "'angular momentum operator "'is one of several related operators analogous to classical angular momentum.
• Within a given subspace, a component of a vector operator will behave in a way proportional to the same component of the angular momentum operator.
• The relationship between angular momentum operators and rotation operators is the same as the relationship between Lie algebras and Lie groups in mathematics, as discussed further below.
• In both cases the angular momentum operator uncertainty relation this means that the angular momentum and the energy ( eigenvalue of the Hamiltonian ) can be measured at the same time.
• We assume that the states of the subsystems can be chosen as eigenstates of their angular momentum operators ( and of their component along any arbitrary " z " axis ).
• In the special case of a single particle with no electric charge and no spin, the orbital angular momentum operator can be written in the position basis as a single vector equation: