Consider a system with 2 spin 1/2 particles. The Hamiltonian is given by:
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Consider a system with 2 spin 1/2 particles. The Hamiltonian is given by:
Consider one dimensional lattice of N particles having a spin of 1 /2 with an associated magnetic moment μ The spins are kept in a magnetic field with magnetic induction B along the z direction. The spin can point either up, t, or down, , relative to the z axis. The energy of particle with spin down is e B and that of particle with spin up is ε--B. We assume that the system is isolated from. its environment so...
1. (30 points). Coupled spins. Spin-1/2 particles A and B evolve under the influence of the following Hamiltonian (for simplicity takeh-1 so that energies are expressed in frequency units): We work in the uncoupled basis aba) Ib), where a,b E 0,1 and where states 0) (1)) correspond to single spins aligned (antialigned) with the z-direction. As we discussed in lecture, the eigenstates of the Hamiltonian are 100), 111), and 2-1/2 (101) 110)). a. We prepare the initial state t01). Since...
(10 points) A spin-1/2 particle is originally in the ground state of the Hamiltonian Ho woS At time t - 0 the system is perturbed by Here and above s, are the spin matrices. Consider H, as a small perturbation of Ho i.e., ao > wi, Find the probability for the particle to flip its spin under the perturbation at t n oo.
Consider a system with spin 1 and spin 1/2 particle. What are the possible total spin values and coefficients?
For a system of two particles with spin 3/2 and 1/2 write out all the possible |j1m1> x |j2m2> states. how many states should exist?
qm 2019.3 3. The Hamiltonian corresponding to the magnetic interaction of a spin 1/2 particle with charge e and mass m in a magnetic field B is À eB B. Ŝ, m where Ŝ are the spin angular momentum operators. You should make use of expres- sions for the spin operators that are given at the end of the question. (i) Write down the energy eigenvalue equation for this particle in a field directed along the y axis, i.e. B...
Starting with the following eigenket for a system of two spin-1/2 particles, obtain the other three eigenkets in the (s,m) representation. 3.
12. Consider five spin-1/2 elementary particles (distinguishable and with no external fields present). What is the probability that four have spin up and the other has spin down, and how many different configurations of the five could give this result?
Consider a harmonic oscillator with Hamiltonian given by ?=(p^2/2m)+(1/2)X^2 = (a+)(a-)+(1/2) The current system state is the superposition of the lowest and next-to-lowest energy eigenstates that gives the most negative possible value for the average position, use raising and lowering operators to derive the average momentum for this state. then, simplify using ħ = ? = 1
1. The aim of this problem set is to understand the dynamics of a spin-1/2 system in its full glory. Note that formally a spin-1/2 system and a qubit are equivalent hence, all what you will discover in this problem set will carry over to single qubits. Consider an electron spin (spin 1/2, magnetic moment gHB) interacting with a strong magnetic field Bo (0,0, B) in the z direction as well as with a much weaker magnetic field Brf =...