1. Given that angular momentum is given by L=(r)(p), the components of the angular momentum can...
1. Given that angular momentum is given by L=(r)(p),
the components of the angular momentum can be found to
be:
Lx=ypz-zpy
Ly=zpx-xpz
Lz=xpy-ypx
(a) What are the corresponding angular momentum
operators Lx, Ly, and
Lz?
(b) write communation relations [Lx,
Ly], [Ly, Lz], and [Lz,
Lx]. What does these expressions say about the ability
to measure components of angular momentum simultaneously?
plz explain part B in depth dont do derivation of commutation
relation explain the second part
also do part a
Homework Answers
Add Answer to:
1. Given that angular momentum is given by L=(r)(p),
the components of the angular momentum can...
(2.) Consider the orbital angular momentum operator defined in terms of the position and momentum operators...
(2.) Consider the orbital angular momentum operator defined in terms of the position and momentum operators as p. Define the angular momentum raising and lowering operators as L± = LztiLy. Use the commutation relations for the position and m omentum operators and find the commutators for: (a.) Lx, Lz and Ly, Lz; (b.) L2, Lz; (c.) L+,L
Classically, orbital angular momentum is given by L = r times p, where p is the...
Classically, orbital angular momentum is given by L = r times p, where p is the linear momentum. To go from classical mechanics to quantum mechanics, replace p by the operator -i nabla (Section 14.6). Show that the quantum mechanical angular momentum operator has Cartesian components L_x = -i (y partial differential/partial differential z - z partial differential/partial differential y L_y = -i(z partial differential/partial differential x - x partial differential/partial differential z L_z = -i (x partial differential/partial differential...
qm 09.4 4. The commutation relations defining the angular momentum operators can be written [Îx, Îy]...
qm 09.4
4. The commutation relations defining the angular momentum operators can be written [Îx, Îy] = iħẢz, with similar equations for cyclic permutations of x, y and z. Angular momentum raising and lowering operators can be defined as În = Îx ihy (i) Show that [Lz, L.] = +ħL. [6 marks] (ii) If øm is an eigenfunction of ł, with eigenvalue mħ, show that the state given by L+øm is also an eigenfunction of L, but with an eigenvalue...
3 Angular Momentum and Spherical Harmonics For a quantum mechanical system that is able to rotate...
3 Angular Momentum and Spherical Harmonics For a quantum mechanical system that is able to rotate in 3D, one can always define a set of angular momentum operators J. Jy, J., often collectively written as a vector J. They must satisfy the commutation relations (, ] = ihſ, , Îu] = ihſ, J., ſu] = ihỈy. (1) In a more condensed notation, we may write [1,1]] = Žiheikh, i, j= 1,2,3 k=1 Here we've used the Levi-Civita symbol, defined as...
Exercise 2:Commutators Given (AB, C) - ABC - ACB + ACB-CAB - ABC] + [A, CJB....
Exercise 2:Commutators Given (AB, C) - ABC - ACB + ACB-CAB - ABC] + [A, CJB. 1- Show that the commutator[L.L]is equal to zero. 2-Computethecommutator(Ly, Lx]. 3-Compute the commutator 3.Lx]. 4-Compute the commutator[LLY.Lx]. 5- Add the results from (2)-(4) to compute [LLyLx]. Lxercise 3: Matrix elements The angular momentum operators acting on the angular momentum eigenstates. Il determined by L-11.m) = (1 + 1) - m(m + 1)2.m +1) L_11.m) = /(1+1) - mm - 1)/1.m-1) L211,m) = hm|1,m) 1-...
4. If the general angular momentum quantum number j is 1 there is a triplet of |j, mj) states 1,1, 1,0), and 1,-1) In this case a matrix representation for the operators J, Jj and J, can be construct...
4. If the general angular momentum quantum number j is 1 there is a triplet of |j, mj) states 1,1, 1,0), and 1,-1) In this case a matrix representation for the operators J, Jj and J, can be constructed if we represent the lj,m,) triplet by three component column vectors as follows 0 0 0 0 0 Jz can then be represented by the matrix: 00 1 (a) Construct matrix representations for the raising and lowering operators, J and J...
A. Issues [1] In addition to damages for one year's notice period, can a trial judge...
A. Issues [1] In addition to damages for one year's notice period, can a trial judge award significant damages for the mere fact of an employee's dismissal, or for the stigma that that dismissal brings? Or for the employer thereafter competing with the ex-employee for the clients, before the ex-employee has got a new job? B. Basic Facts [2] This is an appeal from 2009 ABQB 591 (CanLII), 473 A.R. 254. [3] Usually a judgment recites facts before law. But...
(2.) Consider the orbital angular momentum operator defined in terms of the position and momentum operators as p. Define the angular momentum raising and lowering operators as L± = LztiLy. Use the commutation relations for the position and m omentum operators and find the commutators for: (a.) Lx, Lz and Ly, Lz; (b.) L2, Lz; (c.) L+,L
Classically, orbital angular momentum is given by L = r times p, where p is the linear momentum. To go from classical mechanics to quantum mechanics, replace p by the operator -i nabla (Section 14.6). Show that the quantum mechanical angular momentum operator has Cartesian components L_x = -i (y partial differential/partial differential z - z partial differential/partial differential y L_y = -i(z partial differential/partial differential x - x partial differential/partial differential z L_z = -i (x partial differential/partial differential...
qm 09.4
4. The commutation relations defining the angular momentum operators can be written [Îx, Îy] = iħẢz, with similar equations for cyclic permutations of x, y and z. Angular momentum raising and lowering operators can be defined as În = Îx ihy (i) Show that [Lz, L.] = +ħL. [6 marks] (ii) If øm is an eigenfunction of ł, with eigenvalue mħ, show that the state given by L+øm is also an eigenfunction of L, but with an eigenvalue...
3 Angular Momentum and Spherical Harmonics For a quantum mechanical system that is able to rotate in 3D, one can always define a set of angular momentum operators J. Jy, J., often collectively written as a vector J. They must satisfy the commutation relations (, ] = ihſ, , Îu] = ihſ, J., ſu] = ihỈy. (1) In a more condensed notation, we may write [1,1]] = Žiheikh, i, j= 1,2,3 k=1 Here we've used the Levi-Civita symbol, defined as...
Exercise 2:Commutators Given (AB, C) - ABC - ACB + ACB-CAB - ABC] + [A, CJB. 1- Show that the commutator[L.L]is equal to zero. 2-Computethecommutator(Ly, Lx]. 3-Compute the commutator 3.Lx]. 4-Compute the commutator[LLY.Lx]. 5- Add the results from (2)-(4) to compute [LLyLx]. Lxercise 3: Matrix elements The angular momentum operators acting on the angular momentum eigenstates. Il determined by L-11.m) = (1 + 1) - m(m + 1)2.m +1) L_11.m) = /(1+1) - mm - 1)/1.m-1) L211,m) = hm|1,m) 1-...
4. If the general angular momentum quantum number j is 1 there is a triplet of |j, mj) states 1,1, 1,0), and 1,-1) In this case a matrix representation for the operators J, Jj and J, can be constructed if we represent the lj,m,) triplet by three component column vectors as follows 0 0 0 0 0 Jz can then be represented by the matrix: 00 1 (a) Construct matrix representations for the raising and lowering operators, J and J...
A. Issues [1] In addition to damages for one year's notice period, can a trial judge award significant damages for the mere fact of an employee's dismissal, or for the stigma that that dismissal brings? Or for the employer thereafter competing with the ex-employee for the clients, before the ex-employee has got a new job? B. Basic Facts [2] This is an appeal from 2009 ABQB 591 (CanLII), 473 A.R. 254. [3] Usually a judgment recites facts before law. But...
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