GATE Physics Exam > GATE Physics Videos > Quantum Mechanics for GATE > Lecture 2: Angular Momentum Operator
Lecture 2: Angular Momentum Operator Video Lecture | Quantum Mechanics for GATE - GATE Physics
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FAQs on Lecture 2: Angular Momentum Operator Video Lecture - Quantum Mechanics for GATE - GATE Physics
| 1. What is the definition of the angular momentum operator in quantum mechanics? |  |
Ans. The angular momentum operator in quantum mechanics is a mathematical operator that corresponds to the classical angular momentum of a physical system. It is denoted by the symbol L and is used to describe the rotational motion of particles.
| 2. How is the angular momentum operator related to the position and momentum operators? | |
Ans. The angular momentum operator can be expressed in terms of the position and momentum operators as L = r x p, where r is the position vector and p is the momentum vector. This relationship helps in understanding the quantum mechanical properties of angular momentum.
| 3. What are the eigenvalues and eigenvectors of the angular momentum operator? | |
Ans. The eigenvalues of the angular momentum operator represent the possible values of angular momentum that a system can have, while the eigenvectors correspond to the states of the system with definite angular momentum values. In quantum mechanics, the eigenvalues are quantized and can only take on specific discrete values.
| 4. How does the angular momentum operator behave under rotations? | |
Ans. The angular momentum operator is said to be a vector operator because it transforms like a vector under rotations. This means that its components change according to the rules of vector addition and subtraction when the coordinate system is rotated.
| 5. Can the angular momentum operator commute with other operators in quantum mechanics? | |
Ans. The angular momentum operator does not generally commute with other operators in quantum mechanics. This non-commutativity leads to interesting consequences such as the uncertainty principle for angular momentum, which states that the measurement of one component of angular momentum affects the precision of the measurement of another component.
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Dec 22, 2024 Last updated |
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