Topics are presented in an order so that new concepts are introduced and relevant formulas are derived in ways arising naturally in the treatment rather than by appealing to unfamiliar concepts or ud hoc methods. Modern notation and terminology are used in a geometric and algebraic approach. Some concepts of group theory are introduced and are related to this approach, but knowledge of group theory is not required. Those who plan to use continuous groups that are more abstract than the rotation group may thereby develop their insight and skills by practicing with rotations. I try to distinguish carefully results that depend only on rotational symmetry and are generally valid from those having their most fruitful interpretation from the viewpoint of quantum mechanics. Applications to quantum mechanics therefore usually appear toward the end of sections and chapters.
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Posted: September 4th, 2008, 7:33am CEST
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If a physical system has only internal interactions and if space is isotropic, then intrinsic properties of the system must be independent of its orientation and must be indistinguishable in all directions. From this fundamental rotational symmetry concept the theory of angular momentum has been developed into a sophisticated analytical and computational technique, especially when applied to quantum mechanics. I aim in this book to develop angular momentum theory in a pedagogically consistent way, starting from the geometrical concept of rotational invariance rather than from the dynamical idea of orbital angular momentum and its quantization. The latter approach, though hallowed by tradition, needlessly confuses quantum mechanics with geometry.
Topics are presented in an order so that new concepts are introduced and relevant formulas are derived in ways arising naturally in the treatment rather than by appealing to unfamiliar concepts or ud hoc methods. Modern notation and terminology are used in a geometric and algebraic approach. Some concepts of group theory are introduced and are related to this approach, but knowledge of group theory is not required. Those who plan to use continuous groups that are more abstract than the rotation group may thereby develop their insight and skills by practicing with rotations. I try to distinguish carefully results that depend only on rotational symmetry and are generally valid from those having their most fruitful interpretation from the viewpoint of quantum mechanics. Applications to quantum mechanics therefore usually appear toward the end of sections and chapters.
Topics are presented in an order so that new concepts are introduced and relevant formulas are derived in ways arising naturally in the treatment rather than by appealing to unfamiliar concepts or ud hoc methods. Modern notation and terminology are used in a geometric and algebraic approach. Some concepts of group theory are introduced and are related to this approach, but knowledge of group theory is not required. Those who plan to use continuous groups that are more abstract than the rotation group may thereby develop their insight and skills by practicing with rotations. I try to distinguish carefully results that depend only on rotational symmetry and are generally valid from those having their most fruitful interpretation from the viewpoint of quantum mechanics. Applications to quantum mechanics therefore usually appear toward the end of sections and chapters.
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