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jc09
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Homework Statement
Show that [ Lk , r^2] = 0
Homework Equations
The Attempt at a Solution
know that L=r x p=r x(-ih(bar)V)
How to Demonstrate [Lk, r^2] = 0?
- Thread starter jc09
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SUMMARY
The discussion focuses on demonstrating that the commutator [Lk, r^2] equals zero, where L represents angular momentum and r^2 is the square of the position vector. The participant clarifies that L can be expressed as L = r x p, with p being the momentum operator. The solution involves breaking down the commutator into three parts: [Lz, x^2], [Lz, y^2], and [Lz, z^2], which are to be calculated individually to confirm that their sum results in zero.
PREREQUISITES- Understanding of angular momentum operators in quantum mechanics
- Familiarity with commutation relations
- Knowledge of position and momentum operators
- Basic grasp of vector calculus and cross products
- Study the derivation of angular momentum operators in quantum mechanics
- Learn about commutation relations and their implications in quantum mechanics
- Explore the properties of the position operator in quantum mechanics
- Investigate the significance of the commutator in quantum mechanics
Students and professionals in quantum mechanics, particularly those studying angular momentum and commutation relations, will benefit from this discussion.
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