Which one of the following equation is correct for angular momentum operator?
Answers
Answer:
jogfiososo
Explanation:
jqjajajajajwjhw
Introduction
Angular momentum plays a central role in both classical and quantum mechanics. In
classical mechanics, all isolated systems conserve angular momentum (as well as energy and
linear momentum); this fact reduces considerably the amount of work required in calculating
trajectories of planets, rotation of rigid bodies, and many more.
Similarly, in quantum mechanics, angular momentum plays a central role in under-
standing the structure of atoms, as well as other quantum problems that involve rotational
symmetry.
Like other observable quantities, angular momentum is described in QM by an operator.
This is in fact a vector operator, similar to momentum operator. However, as we will
shortly see, contrary to the linear momentum operator, the three components of the angular
momentum operator do not commute.
In QM, there are several angular momentum operators: the total angular momentum
(usually denoted by J~), the orbital angular momentum (usually denoted by L~ ) and the
intrinsic, or spin angular momentum (denoted by S~). This last one (spin) has no classical
analogue. Confusingly, the term “angular momentum” can refer to either the total angular
momentum, or to the orbital angular momentum.
The classical definition of the orbital angular momentum, L~ = ~r × ~p can be carried
directly to QM by reinterpreting ~r and ~p as the operators associated with the position and
the linear momentum.
The spin operator, S, represents another type of angular momentum, associated with
“intrinsic rotation” of a particle around an axis; Spin is an intrinsic property of a particleIntroduction
Angular momentum plays a central role in both classical and quantum mechanics. In
classical mechanics, all isolated systems conserve angular momentum (as well as energy and
linear momentum); this fact reduces considerably the amount of work required in calculating
trajectories of planets, rotation of rigid bodies, and many more.
Similarly, in quantum mechanics, angular momentum plays a central role in under-
standing the structure of atoms, as well as other quantum problems that involve rotational
symmetry.
Like other observable quantities, angular momentum is described in QM by an operator.
This is in fact a vector operator, similar to momentum operator. However, as we will
shortly see, contrary to the linear momentum operator, the three components of the angular
momentum operator do not commute.
In QM, there are several angular momentum operators: the total angular momentum
(usually denoted by J~), the orbital angular momentum (usually denoted by L~ ) and the
intrinsic, or spin angular momentum (denoted by S~). This last one (spin) has no classical
analogue. Confusingly, the term “angular momentum” can refer to either the total angular
momentum, or to the orbital angular momentum.
The classical definition of the orbital angular momentum, L~ = ~r × ~p can be carried
directly to QM by reinterpreting ~r and ~p as the operators associated with the position and
the linear momentum.
The spin operator, S, represents another type of angular momentum, associated with
“intrinsic rotation” of a particle around an axis; Spin is an intrinsic property of a particle