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ythaaa
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Hi, just wondering whether the commutation relation [tex][\phi,L_3]=i\hbar[/tex] holds and similar uncertainty relation such as involving X and Px can be derived ?
thanks
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The commutation relation for L_{3} and phi is given by [L_{3}, phi] = iℏℏsin(phi).
The commutation relation is derived using the principles of quantum mechanics, specifically the quantum mechanical operators for angular momentum (L_{3}) and position (phi).
The commutation relation tells us that L_{3} and phi do not commute, meaning that their order matters when performing calculations. This is a fundamental concept in quantum mechanics and has important implications for the uncertainty principle.
The commutation relation is closely related to the uncertainty principle, which states that certain pairs of physical properties, such as position and momentum, cannot be known simultaneously with complete precision. The commutation relation for L_{3} and phi is one example of this principle in action.
Yes, the commutation relation is a general concept in quantum mechanics and can be applied to other operators as well. It is an important tool for understanding the behavior of quantum systems and making predictions about their properties.