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- 5 Angular Momentum - University of Cambridge
angular momentum is similar to the role of Aand Ayfor energy of the harmonic oscillator Again, J + and J are often called raising and lowering operators Their role is to rotate our system, aligning more or less of its total angular momentum along the z-axis without changing the total angular momentum available (See gure7 )
- Chapter 9 Angular Momentum Quantum Mechanical Angular . . .
tion space components, other components of angular momentum can be shown not to commute similarly Example 9{2: What is equation (9{1) in the momentum basis? In momentum space, the operators are X ! i„h @ @p x; Y ! i„h @ @p y; and Z ! i„h @ @p z; and P x! p x; P y! p y; and P z! p z: Equation (9{1) in momentum space would be written fl
- Quantum Physics II, Lecture Notes 9 - MIT OpenCourseWare
The classical angular momentum operator is orthogonal to both lr and p as it is built from the cross product of these two vectors Happily, these properties also hold for the quantum angular momentum Take for example the dot product of r with L to get r · L = xˆ ˆ i Li = xˆiǫijk xˆj pˆk = ǫijk xˆi xˆj pˆk = 0 (1 27)
- Lecture 14 Angular momentum operator algebra
Angular momentum operator algebra In this lecture we present the theory of angular momentum operator algebra in quantum mechanics 14 1 Basic relations Consider the three Hermitian angular momentum operators J^ x;J^ y and J^ z, which satisfy the commutation relations J^ x;J^ y = i~J^ z; J^ z;J^ x = i~J^ y; J^ y;J^ z = i~J^ x: (14 1) The
- Chapter 13. Angular Momentum: General Theory - UC Santa Barbara
In quantum me-chanics, we encounter two kinds of angular momenta The orbital angular momentum is similar to the angular momentum in classical mechanics, which is defined by where ~r is the position of a particle and ~p is its momentum
- Understanding exception to: Two non-commuting Hermitian . . .
However, the central force problem has states (S states) for which the non-commuting angular momentum operators all have simultaneous eigenstates with eigenvalue zero You should consider why an eigenvalue of zero for the non-commuting operators enables this
- Lecture 8: Angular momentum and rotation operators
8-4 Lecture 8: Angular momentum and rotation operators The commutator relations [J z;J] = ~J suggested that J is a \ladder operator" that raises (J +) or lowers (J) the eigenvalue of J z by a unit of ~ In order to show this, we consider J z(J ja;bi) = ([J z;J] + J J z)ja;bi = ( ~J + J b)ja;bi = (b ~)(J ja;bi)) J ja;bi = C (a;b)ja;b ~i:
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