Question

In: Physics

Angular momentum: Let the Hamiltonian of our particle be described as H = ??^2 where J...

Angular momentum: Let the Hamiltonian of our particle be described as H = ??^2 where J is the angular momentum operator. a) Diagonalise the Hamiltonian for j=0,1

b) Use explicit form of J+ and J- rising and lowering operators and Jz operator to obtain the 4 lowest energy levels for j=0,1 .

Solutions

Expert Solution


Related Solutions

(4) Consider a system described by the Hamiltonian H, H = 0 a a 0 !,...
(4) Consider a system described by the Hamiltonian H, H = 0 a a 0 !, where a is a constant. (a) At t = 0, we measure the energy of the system, what possible values will we obtain? (b) At later time t, we measure the energy again, how is it related to its value we obtain at t = 0 ? (c) If at t = 0, the system is equally likely to be in its two possible...
Consider the Hamiltonian of a particle in one-dimensional problem defined by: H = 1 2m P...
Consider the Hamiltonian of a particle in one-dimensional problem defined by: H = 1 2m P 2 + V (X) where X and P are the position and linear momentum operators, and they satisfy the commutation relation: [X, P] = i¯h The eigenvectors of H are denoted by |φn >; where n is a discrete index H|φn >= En|φn > (a) Show that < φn|P|φm >= α < φn|X|φm > and find α. Hint: Consider the commutator [X, H] (b)...
1) What is the direction of the angular momentum for the rotation of the Earth? 2)...
1) What is the direction of the angular momentum for the rotation of the Earth? 2) If you give a hard boiled egg a spin on the table, it will keep spinning for a long time. If you do the same with an uncooked egg, it stops relatively quickly. Explain this. 3) A dumbbell consists of two uniform spheres of mass M and radius R, joined by a thin rod of radius r and length l and mass m. a)...
1. What is the direction of the angular momentum for the rotation of the Earth? 2....
1. What is the direction of the angular momentum for the rotation of the Earth? 2. If you give a hard boiled egg a spin on the table, it will keep spinning for a long time. If you do the same with an uncooked egg, it stops relatively quickly. Explain this. 3. A dumbbell consists of two uniform spheres of mass M and radius R, joined by a thin rod of radius r and length l and mass m. a)...
Let G, H be groups and define the relation ∼= where G ∼= H if there...
Let G, H be groups and define the relation ∼= where G ∼= H if there is an isomorphism ϕ : G → H. (i) Show that the relation ∼= is an equivalence relation on the set of all groups. (ii) Give an example of two different groups that are related.
Calculate the coupled eigenstates that result from the coupling of orbital angular momentum ?=2 with spin...
Calculate the coupled eigenstates that result from the coupling of orbital angular momentum ?=2 with spin angular momentum ?=1/2. HINT: You may freely use results from Ch. 7 in N. Zettili’s book, including results from the solved problems. Simply quote exactly which result you are using each time.
1 Write down the expressions for centripetal force and angular momentum 2 What are the units...
1 Write down the expressions for centripetal force and angular momentum 2 What are the units of moment of inertia? 3 In Fig.1 show that the tension, T, in the string causing the pulley to rotate is given by T = m(g-a) where a is the linear acceleration of the falling mass. 4 In part III, what factors could cause the angular momentum not to be conserved?
(2) Let Vabc = [ - 5 , 5 + 5 j , - 5 j...
(2) Let Vabc = [ - 5 , 5 + 5 j , - 5 j ] T and calculate Vb012. Draw a phasor diagram illustrating the relationship Vb = Vb0 + Vb1 + Vb2 .
Consider the Hamiltonian H, namely, H=A(Jz,1 +Jz,2)+BJ1 ·J2 for a system of two particles in which...
Consider the Hamiltonian H, namely, H=A(Jz,1 +Jz,2)+BJ1 ·J2 for a system of two particles in which the first particle has a spin of 3/2 (j1), and the other has a spin of 1/2 (j2). a) Compute the Hamiltonian matrix in the |j1j2;m1m2⟩ basis. (Hint: Be sure to rewrite ˆˆˆˆ the J1 · J2 operator in terms of J±,i and Jz,i.) Is your matrix diagonal? b) Determine the eigenvalues of the matrix you found in a). c) Now compute the Hamiltonian...
Problem 2: A particle with charge q is emitted from the origin with momentum p directed...
Problem 2: A particle with charge q is emitted from the origin with momentum p directed at an angle ? to a uniform magnetic field B which lies in the z-direction. i) What is the position of the particle as a function of time? ii) At what point does the particle next intersect the z-axis?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT