Operating on spin angular momenta

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SUMMARY

The discussion focuses on the operations of raising and lowering angular momentum in quantum mechanics, specifically concerning spin states. The operations S_(upward spin & upward spin) and S_(downward spin & upward spin) are explored, emphasizing that these operations modify the projection of angular momentum along a fixed axis, typically the Z-axis. It is established that the length of the angular momentum vector remains constant, with only discrete projections being possible due to quantum mechanics. The conversation highlights the need for a physical understanding of these operations to grasp their implications fully.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with angular momentum and spin concepts
  • Knowledge of discrete vs. continuous projections in physics
  • Basic grasp of vector operations in quantum systems
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  • Study the mathematical formulation of angular momentum in quantum mechanics
  • Learn about the role of the Z-axis in quantum spin operations
  • Explore the implications of discrete projections in quantum systems
  • Investigate specific examples of raising and lowering operators in quantum mechanics
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Students and professionals in physics, particularly those focusing on quantum mechanics, as well as educators seeking to explain angular momentum operations effectively.

runninglow
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how am i supposed to carry out say, a lowering operation?for example:S_(upward spin & upward spin) or S_(downward spin & upward spin). and raising or lowering a combination of spin,what do they mean anyway?i want the physical feel of the situation.
 
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raising and lowering of spin and angular momenta should be quite intuitive I guess, that it is an operation which increases or decreases the projection of a certain angular momentum about a fixed axis (the standard in almost all quantum mechanics is that one has the Z-axis as reference).

The length of the angular momentum vector is always fixed, and due to quantum mechanics, only certain projections on axes are possible (c.f with a "classical" vector which can have a continuous setup of projections)

A rasing, or lowering, operation just changes that projection, but of course by a disctrete amount.

If you want, provide a specific situation where you have trouble, and we'll try to help you.
 

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